"subject to" financing

[William Leahy]

Hi Folks, Say I purchase a property from a relative, pay them their equity receve the deed in my name and assume the payment of their mortage Subject to. 

I understand that the original mortgage is non assumable and that the bank could trigger the due on sale. What are the other potential pitfalls. Do I lose tax benefits since the mortgage interestt documents are not in my name. Should I just bite the bullet and refi? Thank you