We construct aﾠq-analog of the blossom for analytic functions, the analyticﾠq-blossom. Thisﾠq-analog also extends the notion ofﾠq-blossoming from polynomials to analytic functions. We then apply this analyticﾠq-blossom to derive identities for analytic functions represented in terms of theﾠq-Poisson basis, includingﾠq-versions of the Marsden identity and the de Boor-Fix formula for analytic functions.