there are differences between ESA and Service Pets so I'm trying to understand what are the different proof the landlord will ask

It is really the Trustee who orders the sale based on notice and proof from the Mortgagee of default.

But as I said, if you have any proof, I’m happy to look at it and admit if I’m wrong.  

When we get farther into this process, I will absolutely ask to see all the leases and proof of payment history for the current tenants. 

A few tips: maintain a solid credit score, organize your financials (especially your proof of funds), and be ready to show that you have a solid plan for your investments.

Of course you want to pay attention to market cycles etc.

Assorted things.Realistically, on a triplex that's not fully rehabbed, without assuming tenant damages I'd be factoring in roof, flooring, HVAC at minimum on nothing more than a 10 year cycle (5 is safer).

I ask for a record of past deals that went full cycle and deals that are pending and deals in the pipeline.

They will almost certainly demand a proof of funds letter too.

If the evidence does not pass all of those hurdles, we have a form letter that they have not provided sufficient proof of an ESA.