Representing Dehn twists with branched coverings

We show that any homologically non-trivial Dehn twist of a compact surface $F$ with boundary is the lifting of a half-twist in the braid group ${cal B}_{n}$, with respect to a suitable branched covering $p : F o B^2$. In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on $B^2$ is a branched covering of $B^2 imes B^2$.