Most landlord insurance policies exclude pitbull pets. You would need to get a separate insurance policy that covers you and the landlord for issues related to your pet. These are 300-400 per year and depend on the history of your pet. If you are unable to find these in a Google search let me know and I'll provide you some names.
Many owners are not aware of this exclusion, those that are often unaware there are stand alone pet insurance policies to protect them. In many instances you will need to educate the landlord.