What happens when I reiterate a time spiral? I know the reiterate will come back to hand, I'm just wondering if it will get shuffled away before I can cast it again.
So, Time Spiral is on the stack and you have priority. You cast Reiterate and both players pass priority. Reiterate resolves so now you have the original Time Spiral on the stack with a copy above it and Reiterate in your hand. You can, if you have the mana, cast Reiterate again creating another copy of Time Spiral.
Note that the lands don't untap until Time Spiral resolves and when Time Spiral Resolves, you will shuffle away Reiterate. Then, in the middle of each Time Spiral resolving, you can only cast Instants or spells with Flash until the final Time Spiral resolves.
Reiterate
Time Spiral
So, Time Spiral is on the stack and you have priority. You cast Reiterate and both players pass priority. Reiterate resolves so now you have the original Time Spiral on the stack with a copy above it and Reiterate in your hand. You can, if you have the mana, cast Reiterate again creating another copy of Time Spiral.
Note that the lands don't untap until Time Spiral resolves and when Time Spiral Resolves, you will shuffle away Reiterate. Then, in the middle of each Time Spiral resolving, you can only cast Instants or spells with Flash until the final Time Spiral resolves.