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,
Guéritaud-Futer (who recently improved previous work
of Lackenby), and Futer-Kalfagianni-Purcell, and it comes
in two versions: a weaker general form and a shaper form.
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.