"Analyzing" is the American English spelling, while "analysing" is the British English version. Both come from "analyze/analyse," and the difference is just that extra "s" versus "z." In the US, "analyzing" is standard; in the UK, Australia, or other Commonwealth spots, "analysing" is the norm.
Choose based on who’s reading it. If you’re American or aiming for a US audience, go with "analyzing." If you’re British or writing for a UK crowd, "analysing" fits. Practically, they’re interchangeable—meaning’s clear either way. No one’s grading your spelling here unless you’re in a style guide cage match.