Howdy! I am a college student and I am moving from my semester housing to summer housing some time in the next week. If I take all of the water out of my tank and put it in buckets to move the tank, and then put it all back in, will the nitrogen cycle restart? I am only moving across campus, so moving the tank would only be about 10-15 minutes. Thanks!
Former college student here who has moved with an axolotl multiple times (I don't recommend it in general, but obviously it must be done sometimes): do not bother toting buckets of water. The amount of bacteria in the water itself is negligible anyway. The only water you NEED is in the transport tub for your axolotl. As recommended above, I would also put the filter and decor in a small bucket of water to keep everything wet, though for such a short trip you probably wouldn't even need that. Do not underestimate, however, the length of time you will need to set up everything again though. If you are in a warmer climate, definitely have a plan for keeping temperatures as low as possible to reduce stress.
Provided you don't kill your bacteria with chlorine or something, you shouldn't have to worry about the cycle, but I would recommend keeping an eye on your levels for a week or two after moving just to be extra safe. I've done short moves like yours and longer moves of up to 4 hours (including set up) and never had a problem.