  We consider two necessary and sufficient conditions for macrorealism recently
appeared in the literature, known as no-signaling-in-time and arrow-of-time
conditions, respectively, and study them in the context of neutrino flavor
transitions, within both the plane wave description and the wave packet
approach. We then compare the outcome of the above investigation with the
implication of various formulations of Leggett--Garg inequalities. In
particular, we show that the fulfillment of the addressed conditions for
macrorealism in neutrino oscillations implies the fulfillment of Leggett--Garg
inequalities, whereas the converse is not true. Finally, in the framework of
wave packet approach, we also prove that, for distances longer than the
coherence length, the no-signaling-in-time condition is always violated whilst
Leggett--Garg inequalities are not.
