Cats and Dogs and Snakes, Oh My!
Pet Friendly Apartment Searching

First Category - Landlord Doesn't Care
Neither do they really care about you, nor do they care about the quality and condition of the apartment they offer you. All they care about is timely rent payment, and whether the market is hot enough to support this bastard attitude of theirs.
As long as the rent is paid on time, they would not care if a bull moose is living in the apartment with you. When you move out of the apartment, Fido may have destroyed the floor, FiFi may have shed eight pounds of dander, Fergie your roommate's anaconda may be living in the walls.
Landlord doesn't care. The next group of tenants will have to inherit that mess. You will see this first hand when you are the tenant inheriting the mess. The first category of pet friendly apartments is a complete "I don't care" scenario. When quality is no object, then this category is for you.
Hint: apartments in this category can be found by doing a cross-referenced search for Dog Friendly and No Pet Deposit.