Moving does NOT mean you have to give up your pet! If you need to move for any reason, PLEASE DO NOT leave your pet behind or abandon them on to the streets/desert assuming someone will find them in time (95% of the animals left behind die of starvation, killed by cars or other animals). You loved your pet enough to take him/her in please don't give up on them now, there are many resources here to help you. This article is a great resource: Renting with Your Dog.
The following resources are available to help you find pet friendly rentals:
If you own a pitbull please don't give your dog up assuming you won't be able to find a rental that will accept your dog. Click on this link, your pitbull's life may depend on it... http://www.mypitbullisfamily.com/arizona.html