If I purchase (read: finance) a home in a state other then where I am
currently residing, for personal not rental use, what can I write off
on my taxes?

I would like to purchase a home in a market that is cheaper than where
I currently live, with the intention to move there in a year or two. 
I would maintain an apartment where I currently reside and I would
improve the home and pay it down until i am ready to move in to it.

Dear Lookingforahome, 

Your question is about to expire without having been answered, and you
might be disappointed.

A possible reason for that could be your pricing, which might be a bit
low for the type of research requested. Here is a link to guidelines
about pricing your question, in the pricing guide:
https://answers.google.com/answers/pricing.html - I hope this would
help you price your next questions on Google Answers.