buying third property

[Tripp Wylie]

New to Bigger Pockets and excited about what I've seen and read so far.  

I currently have two properties.  One is listed as my primary residence because I lived there for a few years but now I rent it out to tenants.  I also bought a second home because I thought I was changing jobs and moving.  However, a different opportunity fell in my lap and I'll be in a different city and looking to buy and make it my primary residence.

My question is this: if i have the two properties mentioned above rented out does the bank waive those mortgage payments so they don't count against my debt to income ratio?  Do I have to showed signed leases?  Have tax returns? etc?