  Let $p: S\to S_g$ be a finite covering of an orientable closed surface of
genus $g$. We prove that, for $g\geq 3$, the rational homology group
$H_1(S;{\mathbb Q})$ is generated by cycles supported on simple closed curves
$\gamma\subset S$ such that $p(\gamma)$ is contained in a $3$-punctured, genus
$0$ subsurface of $S_g$. In particular, this answers positively, for $g\geq 3$
and rational coefficients, a question by Autumn Kent.
