Is it possible to transfer or assume a mortgage put in place by a deceased parent?

my deceased mother has had a mortgage on her home, with bank of america, since 2000. she passed away in 2006 and i inherited her home. i have been paying her mortgage since 2004, two years before her death and have continued to pay the $1403.00/monthly at 6.75% . i would love to refinance and take advantage of the low interest rates but the loan is not in my name. i would also like to take advantage of having the mortgage in my name for tax purposes. is there such a thing as transferring the mortgage from parent to child at the time of death? i am the current owner of the home and can prove that i have been paying monthly for the last 6 years? any help or advice would be greatly appreciated. thank you.