On the New Conditions for a Total Neutrino Conversion in a Medium

We show that the arguments forming the basis for the claim that the conditions for total neutrino conversion derived and studied in detail in [1,2] ``are just the conditions of the parametric resonance of neutrino oscillations supplemented by the requirement that the parametric enhancement be complete'', given in [4] have flaws which make the claim physically questionable. We show also that in the case of the transitions in the Earth of the Earth-core-crossing solar and atmospheric neutrinos the peaks in the relevant transitions probabilities $P_{a b}$, associated with the new conditions, $max P_{a b} = 1$, are of physical relevance - in contrast to what is suggested in [4]. Actually, the enhancement of $P_{a b}$ in any region of the corresponding parameter space are essentially determined by these absolute maxima of $P_{a b}$. We comment on few other aspects of the results derived in [1,2,3] which have been misunderstood and/or misinterpreted in [4].