Honestly, I never tell my apartment management about my reptiles. They do know about my mammalian stuff though.
I always ask before signing the lease, "Do you allow caged pets?" or "I was thinking about getting a small reptile, but not sure yet" to see what their reactions are.
Most places don't have a pet deposit on caged animals anyways, typically only cats or dogs. And cats/dogs are usually the only thing they really care about.

If the apartment says "yes we allow caged animals.", and the don't need to be on the lease then that's usually a good to go for me.

And whenever maintenance comes by, I just shut the door to my rack or cover it with a sheet. By law, they are not allowed to touch anything of yours (aka move sheet/open your stuff) without permission and/or warrant.