  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 B_n, with
respect to a suitable branched covering p : F -> 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 x B^2.
