  The natural parameterization of vacuum oscillations in three neutrino flavors
is studied. Compact and exact relations of its three parameters with the
ordinary three mixing angles and CP violating phase are obtained. Its
usefulness is illustrated by considering various applications: the study of the
flavor ratio and of its uncertainties, the comparison of expectations and
observations in the flavor triangle, the intensity of the signal due to Glashow
resonance. The results in the literature are easily reproduced and in
particular the recently obtained agreement of the observations of IceCube with
the hypothesis of cosmic neutrino oscillations is confirmed. It is argued that
a Gaussian treatment of the errors appropriately describes the effects of the
uncertainties on neutrino oscillation parameters.
