What do you mean "operated" the calendar? Usually when we say "calendar," we mean a culture's method of organizing days and other temporal periods. It's not exactly something one "operates."

Are you talking about physical calendars like the oft adapted Sun Stone? First of all, it's tough to call it rightfully a "calendar." One of the rings (the first one around the four squares in the middle) does contain signs for the 20 days in of a month in the Mesoamerican 365-day calendar, but that is the only properly calendrical imagery. The rest is more cosmological or historical, though, as with most Meseoamerican things, that does tie into calendrical concepts.

But even if it were a calendar, such a thing doesn't need to be "operated." I can't hand you the 12-month calendar off your wall and say "Operate this!" It's a graphical representation of temporal periods, a chart, if you will, that tells you which periods are when. It can be read, for sure, but that didn't seem to be what you were asking. Keeping track of the date and astronomical occurrences was in the job description of many Mesoamerican priests and nobles; one Maya title was aj k'iin, "he of the day/daykeeper." If you'd like to know more about them, do feel free to ask a follow up question!

Regardless of its purpose, there's no reason to suggest anyone was moving it around.