I'm not 100% sure, but most glass pieces come with a storage bag, and I assume that the bag would be long enough to cover the handle too. So I don't think it would be any more difficult to store than a regular glass piece (then again, I don't own one with this type of handle so I could be wrong).
A little extra care should be taken when storing any glass toy, but the twister is not any more difficult to store. It's just a little longer than the other toy.