Let $\Sigma_1$, $\Sigma_2$ be two closed Riemann surfaces, $\pi: \Sigma_1 \to \Sigma_2$ is degree $m$ branched cover of $\Sigma_2$, then we have formula about their Euler number: $$\chi(\Sigma_1)= m\chi(\Sigma_2) - \Sigma_{p \in \Sigma_1}(e_p-1),$$ where $e_p$ is e ramification index at $p$.
Now suppose $\pi: \Sigma_1 \to \Sigma_2$ is still a degree $m$ branched cover of $\Sigma_2$, but $\Sigma_1$, $\Sigma_2$ are punctured Riemann surfaces. If there is a version of Riemann–Hurwitz formula for this case?