Given two applications $f$ and $g$, denote by $R (f, g)$ the set of Reidemeister classes determined by $f$ and $g$ (according to the algebraic definition, on the induced on fundamental groups). And $\operatorname{Lev}(f, g)$ the set of conjugacy classes of lifts of $f$ and $g$ in respect of universal coverings.
I know these two ways of defining classes and Reidemeister number but how do I prove that the cardinal of $\operatorname{Lev}(f, g)$ is equal to $R (f, g)$, ie, they produce the same Reidemeister number?
