  In this paper we deal with Seifert fibre spaces, which are compact
3-manifolds admitting a foliation by circles. We give a combinatorial
description for these manifolds in all the possible cases: orientable,
non-orientable, closed, with boundary. Moreover, we compute a potentially sharp
upper bound for their complexity in terms of the invariants of the
combinatorial description, extending to the non-orientable case results by
Fominykh and Wiest for the orientable case with boundary and by Martelli and
Petronio for the closed orientable case.
