  We consider closed orientable 3-dimensional hyperbolic manifolds which are
cyclic branched coverings of the 3-sphere, with branching set being a
two-bridge knot (or link). We establish two-sided linear bounds depending on
the order of the covering for the Matveev complexity of the covering manifold.
The lower estimate uses the hyperbolic volume and results of Cao-Meyerhoff and
Gueritaud-Futer (who recently improved previous work of Lackenby), while the
upper estimate is based on an explicit triangulation, which also allows us to
give a bound on the Delzant T-invariant of the fundamental group of the
manifold.
