With only a single decklist in the commander archives, Alexi, Zephyr mage is clearly not a very popular gal. She's mono-colored, expensive, slow, and card intensive. But she does have a few very cool, very blue synergies going for her, the greatest of which is also the most expensive - the vaunted timetwister, which is currently in the mail to me for the low, low price of $350. And if I'm picking between boring, cookie-cutter Nekusar or rebellious Alexi to get some use out of my first piece of power, I'm damn sure going with Alexi. And I'm going HARD. Figuratively.
The goal is basically to timetwister as much as possible after bouncing everyone else's creatures to their hands. Counterspells control what needs controlling, recursion lets you get back timetwister, the rogue's gallery gives you CA benefits for the empty field. Ultimately I'm hoping to add a sunder to the mix, leaving you with many turns to pulverize your opponents before they can recover - or infinity turns, if you've got a land equilibrium.
I think cascade is actually going to be a frequent target for tutors. First of all, because it's got a lot of ramp I don't think the cost is an issue. In order to complete my combo I'll need to pump quite a bit of mana into Alexi's ability, which means 7 shouldn't be problem. I'm never going to entwine it. I'm going to shuffle everyone's board into their decks, leaving them creatureless and handless, and then start beating down with the rogue's gallery.
Honestly I'm not that sold on the azami combo wincon. Neither Azami nor MoM are easy to tutor or recur. If that was my only wincon I think it'd be pretty tenuous, although MoM and Azami are both pretty decent on their own, so maybe it could be an alt wincon or something, although lab maniac is pretty worthless without them. I guess psychosis crawler is decent with wheels (except cascade obviously). Anyway it's also true that it seems less fun. Although to be fair I think this deck is going to piss off a lot of people anyway.
Initial testing makes me think the absolute backbreaker cards are going to be land equilibrium and sunder. Going T2 rock, T3 equilibrium utterly dismantles some (bad) decks, and I have enough rocks to eventually cast anything in the deck. Even more ridiculous with a sol ring/mana crypt into a T2 equilibrium. And of course a mass bounce followed by sunder is brutal as well, even if it's not followed by a timetwister. To be honest I think I'll frequently want to tutor sunder instead of twister since people can't recast their creatures without land anyway.
Overall, I think you'd be better off going UR or UBR because you'll have access to all the handcycling cards and more options for removal and tutors. My primer build uses the bounce-cycle strategy to great effect, primarily focusing on Cyclonic Rift as the bouncer, but Devastation Tide and Evacuation could also be added. Boomerang is an efficient option too.
It's worth saying that I feel that your strategy is a bit flawed in that your end goal seems to be the bounce-cycle. What happens if you face a non-creature based deck such as Niv-Mizzet or Nekusar? Suddenly your commander is worthless. Also, if your rogues get bounced by an enemy Cyclonic Rift, how do you plan on dealing damage to win? You really need an infinite turn combo or something like Laboratory Maniac.
I'm running Alexi because she's unique and uncommon, my goal here isn't to build the best deck I can (did that already, years ago, turns out everyone hates it when I do that) but to execute the bounce + cycle strategy as well as I can. Niv (and nekusar) are horrendously overplayed and not only bore me to tears but also draw loads of hate. The fun in this deck is going to be playing a completely unheard of general, everyone totally discounting her for being old and janky, and then suddenly taking everyone by surprise by tucking their board into their deck and beating them to death. Anyway, I'd much much rather try something new and possibly fail than try the same thing everyone else has and succeed. I know how to succeed. Succeeding in someone else's footsteps is boring. I want to try something new.
I don't really see the benefit to going noncreature, my ability to keep the enemy field clear, and thus turn a 3-drop into a damage-plus-CA-engine, is just taking advantage of what my deck does best imo. Thought reflection is expensive and clunky. I expect my rogues to get killed when I'm helping my opponents draw into removal, but that's fine, they'll just get shuffled into my deck next time I timetwister and I can easily recast them for 3-4 mana when I draw them again. If I'm committing big mana to expensive stuff like thought reflection it will be much harder to keep the cycle going smoothly I think. There's no need to get maximum effect for your card when you plan to draw more cards that you'll ever be able to cast - it's more important to have cheap creatures you can cast around other, more crucial stuff.
Cyclonic rift is certainly good for this deck, but I'm no fan of devastation tide or evacuation since the whole point of bounce + timetwister is for the bounce to be asymmetrical. Boomerang and cousins might make it into the deck, we'll see how dangerous other artifacts and enchantments are. I feel like I'd rather run more tutors for cyclonic, though, so I can bounce them all at once. Admittedly that's a bit slower and clunkier but it means I can save a lot more slots as the tutors are flexible.
Helm of awakening would be a nightmare for a deck like this, I'm already giving other people lots of draw, giving them ramp would be suicidal. SDT is kind of mediocre here I think, as I'll be drawing too much for it to make much difference after the early game. Future sight is ok, it's sort of the midpoint between scroll thief and thought reflection in terms of cost and drawing power, but it also shows everyone all my draws which I'm not a fan of.
lab maniac is hard to pull off with timetwister, unless I'm running some infinite combo to enable it. In which case it seems like I may as well just play azami instead of alexi and forget about timetwister entirely, which defeats the point. Again, I know there are better decks, but my goal is to make the best possible version of THIS deck. And a big part of it being THIS deck is that I'm not trying to draw attention to myself with well-known, linear combos.
snappy is good but I don't like the way he exiles the intended target. Giving me a body is nice compared to relearn, but at least conceptually I dislike the idea of exiling timetwister and cutting myself off of my engine.
There are a few cards that I think may help you general:
1) Torpor Orb - You are bouncing creatures a lot, which could lead to some overuse of ETB on the opponents side. This makes sure no shenanigans happen.
2) Dictate of Kruphix - Because you are making people replay threats over and over again the cards they see from Dictate aren't as useful, also makes Forbid something.
3) Maybe Karn, Silver Golem or March of the Machines so that you can hit problem non-creature artifacts with your general's ability.
4) Dreamscape Artist. He's a ramp monster in Mono-Blue and will function better the more cards like Dictate that you put in.
5) Arcane Laboratory - Hey I bounced your guys, and you can only play 1 a turn *evil laugh*
Solid ideas, (except for dictate, I hate letting other people draw cards...if timetwister didn't include the draw 7 I'd like it a lot more, but whatcha gonna do). Torpor orb definitely bears thinking about with this sort of deck, though, and Lab would be really funny. Too bad the lab-with-a-body is in white. Dreamscape artist is an interesting idea considering he basically only costs 1 to use. Although on the other hand, I'm not sure it's better than walking atlas. But maybe I should be running atlas too, if I want to dump my hand faster between timetwistings.
This seems like a really fun project deck! It seems like you're running enough ramp that you could use Capsize effectively with the buyback option. This would allow you to target problematic permanents back to the hand before shuffling back to the library and still be able to reuse the effect for when you don't have a mass bounce option. You could also use it to save your own dudes if need be.
I understand why you're using Mox Diamond and Chrome Mox but between the two of those and Lion's Eye Diamond, it seems like you might have too much risk for getting 2 for 1'ed if the artifact doesn't survive. You might want to switch one of those for Sky Diamond.
The only other concern I might have is actually finishing an opponent. The biggest power I'm seeing in the deck is the general at 3, and that's still 7 swings a player if you can keep the board clear enough to get through every turn. Have you considered anything to make a creature a credible threat like maybe Eldrazi Conscription, Quietus Spike, or even Strata Scythe?
Capsize would be ok, but there's no way to keep it in my hand post-wheel (I guess I could with quicken but that's besides the point) so the buyback isn't that exciting.
Goldfish testing has shown me that mox diamond and chrome mox are both extremely good because they're GREAT to have on a wheel. the CA loss is negligible because you're just going to wheel again, and being able to drop a free mana source is crazy powerful. Sky diamond is decent because it's a 2-drop rock, and might replace some other 2-drop rock, but it's nowhere near as good as the moxen. LED is going to be interesting - the plan is to cast timetwister, crack LED with twister on the stack, and then use the mana to cast whatever I draw. Will that be worth it? Not sure, stay tuned. It's definitely cuttable but it seems too interesting to pass up without extensive testing.
finishing an opponent will probably be slow, but if you want a godlike finisher try land equilibrium + sunder. It's a lockdown deck, not a race-to-the-finish deck, and I want to give the deck plenty of time to do what it wants to do before it actually wins - nothing is more disappointing to me than coming up with an interesting concept for a deck that ends up become irrelevant because some other, more banal synergy keeps becoming the better play and forces me to ignore my original idea. The equipment and auras are nice, but when i'm filling my opponents' hands with new cards, many of which may be removal, I don't want to give them fat juicy targets if I can avoid it.
Honestly this deck ended up using the commander, and timetwister, a lot less than anticipated, and tended to prefer sunder, land equilibrium, and cyclonic rift a lot more than either. The deck doesn't really need more timetwisters. I hate helping other people draw cards, I drew my opponents into all sorts of nasty answers that wrecked me when I tried to use timetwister more.
Also I just didn't actually like this deck very much and don't plan on building or playing it again.