You will need to check Arizona laws, but in Connecticut the general test (used by responding patrol officers, and generally about 99.99% accurate) is if you get your mail there, then you live there. If you live there then the landlord must go through the eviction process at court to get you to leave.
However, if your ex-girlfriend wants you gone, you should go. There is no telling what sort of mischief she might decide to stir up if you refuse to leave. It is generally not worth it, even though from your description it seems like you don't have to leave. But you probably should.
Cogito ergo summopere periculosus.
Fiat justitia, ruat coelum.