My experience is that they want to see the income from the property you will be moving from in the form of signed leases. They will also want to see that you have access to a minimum of 6 months of mortgage, insurance and taxes so if you are vacant you don't immediately go into foreclosure.
I did this a few years ago and as long as I could show income from the previous property it was no problem getting another mortgage for my next place.
There are multiple ways this can play out and some of it is dependent on your lender. It should not be too much trouble however.
In my experience (i did the same thing), you will not need to have two years of rental history for it to count. If you have 30% equity in the first property and a signed lease you can usually count the rental income as part of your DTI. If not you will probably have to qualify with both mortgages.
You will have to ensure you work with a direct lender because sometimes banks have overlays that limit what you can do. You may have to shop around when it comes time for the new place.
Hope that helps a bit. Im sure some more knowledgeable people will chime in soon.
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