Buying a house, transfer of leases and deposite?

[Cory M Hill]

I just bought a house, there are tenants upstairs and down currently.  At closing, I received the security deposits and pro-rated rent but was denied the non-refundable pet deposit. I feel like we should also receive the pet deposit as it's part of the lease and connected to the tenants that are now my responsibility. 

Am I entitled to that deposit?