Coincidence Nielsen numbers for covering maps for smooth manifolds

Let be maps between closed smooth manifolds of the same dimension, and let and be finite regular covering maps. If the manifolds are nonorientable, using semi-index, we introduce two new Nielsen numbers. The first one is the Linear Nielsen number NL(f,g), which is a linear combination of the Nielsen numbers of the lifts of f and g. The second one is the Nonlinear Nielsen number NED(f,g). It is the number of certain essential classes whose inverse images by p are inessential Nielsen classes. In fact, N(f,g)=NL(f,g)+NED(f,g), where by abuse of notation, N(f,g) denotes the coincidence Nielsen number defined using semi-index.