We give upper bounds of the Matveev complexities of two-bridge link complements by constructing their spines explicitly. In particular, we determine the complexities for an infinite sequence of two-bridge links corresponding to the continued fractions of the form $[2,1,\dots, 1,2]$. We also give upper bounds for the 3-manifolds obtained as meridian-cyclic branched coverings of the 3-sphere along two-bridge links.
"Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities." Hiroshima Math. J. 46 (2) 149 - 162, July 2016. https://doi.org/10.32917/hmj/1471024946