Can i recognize same interest amounts as expenses from a house i own and rent and a house i own and live in?

You can deduct mortgage interest on a second home as an itemized deduction if it meets all the requirements for deducting mortgage interest.

If you rent out your second home, you must also use it as a home during the year. You must use it more than 14 days or more than 10% of the total days it is rented out, whichever is longer. If you don't use the home long enough, it's considered a rental property. You can then deduct the mortgage interest as a rental expense.

Mortgage interest can only be claimed on a maximum of two homes (main home and a second home).

If you live in a house you can deduct the interest on the mortgage up to $50,000 since the mortgage is less than $750K.  However, I see in part of your question above, " assuming i live in the the property and don't own it - Could i recognize the same amount?"    If you live in the property and you do not own the property, then you would be renting the property from someone else and not eligible to take a federal deduction as rent is not a deductible expense on your federal return. 

Basically, if you own a property, you can deduct the mortgage interest on mortgage amounts up to $750k if the property is for personal use.

If you are renting out the property, then the mortgage interest may be deductible as a rent expense.

If you do not own the property, you do not get a deduction.