Does tenants deposit transfer to new owner?

[Christopher Leday]

Im in the process of getting ready to purchase and finalize on a triplex. Its a 3br 2bth home with (2) 1 br apartments. Of course after renovations are complete I will be going up on rent to be competitive with the going rates. My question is....Does the currents tenants deposit transfer over to me incase of damages or if the tenants leave the place in tiptop shape requesting their deposit upon leaving.