# Germs as equivalence classes

In my understanding, if $$f$$ is holomorphic in a neighborhood $$U$$ of $$w$$, then there is a unique analytic extension from the restriction $$f\vert U$$ to some maximal domain $$D$$, right? If so, why even bother defining a germ as a class of equivalence (besides the technicality of functions with different domains are different functions).