The b-sheeted Galois covering maps over $C^*$ are equivalent to $z\mapsto z^b$.
I wonder if there is an analogous statement for such Galois covers over C except two points $0,1$. Is that true that the b-sheeted Galois cover over $C\backslash \{0,1\}$ is equivalent to $$ (z,w)\in\{ w^b -z(z-1)=0\} \mapsto z \; ? $$
Thank you.