cv.complex variables – Is there a decision procedure for analytic continuation?

Let an analytic element be a power series associated with an open disc of the complex plane over which the series is convergent. W.l.o.g. assume the series is a Taylor expansion about the center of the disc. It is easy to show that analytic continuation is an equivalence relationship between analytic elements. Is there a decision procedure to determine if an analytic element is in a particular equivalence class? Put equivalently, given two analytic elements, is there a way to determine if they are analytic continuations of each other?