The phrase "keeping up on" refers to staying informed or up-to-date about a particular topic or issue. If you're looking for some synonyms to vary your language or express this idea in different ways, some options include "staying abreast of," "keeping tabs on," "monitoring," "tracking," "following," "keeping in touch with," "keeping a finger on the pulse of," and "keeping an eye on." Each of these phrases implies a similar level of attentiveness and engagement with a subject, but can offer a slightly different shade of meaning or tone depending on the context.