All the anwsers below have good advice and Don is absolutely correct in suggesting that you speak to an accountant or a lawyer. Make sure if you have discussions about transfering ownership to you that you have a title search done on the property to make sure their are no liens on the property.
As has already been noted, most mortgages in effect today are not assumable. You'd probably have to refinance the property in your name. However, you can always check with the lender. It's possible (though unlikely) that they'd permit it.
However, practically, you've already taken over the mortgage. Why would you want it in your name? Check with an accountant, but I can envision a number of drawbacks and no benefits. The primary drawback is that you'd now be on the hook for the amount of the mortgage, making it more difficult for you to borrow money for any other purpose. If you're looking at the tax benefits, I don't think there'd be any. You have to be the owner of the property to claim tax benefits, either as an owner-occupant or as a landlord. Taking over a mortgage does not transfer ownership.
If you're thinking of doing it for estate planning purposes, check with an estate planner. He/she probably would suggest some other technique, such as placing the home in a trust.
Again, don't do anything until you talk to an accountant or estate planner so that you and your mom can both accomplish what the two of you want.
Hope that helps.