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When you move them from one cage to another it’s best to keep all the bedding & put that on top if you need to add more in the new cage.
Don’t do any cleaning except spot cleaning any pee for at least a few weeks after the move, preferably before too so everything has her scent on it. It helps to keep the layout similar if you can too.
Do you mean leaving the cage door open when you’re in the room to supervise her? However ham safe you think your room is I would never leave the cage door open if you aren’t in the room with her but if you are there than that’s fine.