It is shown that in the framework of Stueckelberg's manifestly covariant classical and quatum mechanics, a simple model exists for which , for systems with flavor oscillations, beam transport times can be shortened. This phenomenon could account for the OPERA result indicating early arrival times (less than the time of arrival of a light wave) for the transit of a beam of neutrinos. In this model the neutrinos travel almost everywhere at less than light speed. but achieve a time increment in the annihilation-creation processes associated with the oscillations. This mechanism lies at the foundations of Stueckelberg's theory.