"Having up" is a phrase that can be used in a variety of contexts, but it generally means "lifting" or "raising" something. There are a number of synonyms for this phrase, including elevating, hoisting, heaving, lifting, raising, and boosting. Each of these words has its own specific connotation, and they can be used to describe different actions or situations. For example, "elevating" might suggest raising something to a higher level, while "heaving" might suggest using force to lift something heavy. Ultimately, the synonym you choose will depend on the details of the situation you're describing and the tone you want to convey.