  Model-independent description of nonleptonic decays of charmed mesons is a
challenging task due to large nonperturbative effects of strong interactions on
the transition amplitudes. We discuss the equivalence of two different
flavor-$SU(3)$-based descriptions of Cabibbo-favored non-leptonic decays of
charmed mesons to two-pseudoscalars final states including the $\eta$ and
$\eta^\prime$ mesons.
