The coincidence Nielsen number for covering maps for orientable manifolds

Let f, g : M → N be maps between closed orientable manifolds of the same dimension, and let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\,:\,\widetilde M\; \to \;M\;and\;p'\,:\,\;\widetilde N\; \to \;N$$\end{document} be finite regular covering maps. In this paper, we show that the ordinary Nielsen number N(f, g) of f and g, under certain conditions, can be computed as a linear combination of the Nielsen numbers of specific lifts of the pair (f, g) (called Reidemeister representatives). In addition, we present an easier method to select such representatives than direct computations.