Protocol for inheriting tenants

[Curran D Bishop]

I am closing on a small multi-family at the beginning of June. It is a house with three accessory apartments: we'll be living in the main house and keeping the three existing tenants who currently have month-to-month leases. What is the protocol for beginning contact with inherited tenants? My intention is to not initially increase the rent, make some improvements to the efficiency of their HVAC systems (go from ancient oil to high-efficiency gas) and, once I have the work done, increase the rent to compensate. So I'm thinking of keeping them month-to-month until the work is done, and I also want to let them know how I'm planning to proceed going forward (i.e. I'm not going to ask them to leave when their leases are up, increase the rent immediately, etc.). How have you all proceeded in similar situations?