Solution (source code)

= Solution

A covering evenly covers every base point. It is <regular covering map> when deck transformations act transitively on fibres. For a concrete nonregular example, restrict $z\mapsto z^3-3z$ to
$$
\mathbb C\setminus p^{-1}\{-2,2\}\longrightarrow\mathbb C\setminus\{-2,2\}.
$$
It is a surjective three-sheeted unbranched cover with monodromy $S_3$, so its deck <group> is not transitive.