  In dense matter like the Supernovae and at high energy, neutrinos have two
points where the nonadiabatic transitions could occur. With the present values
of the oscillation parameters in the standard three flavor scenario, two
nonadiabatic transitions can be regarded as independent, i.e., two can be
treated by the two flavor formalism separately. However, in the presence of new
physics, it is not clear in general whether such independence holds. We examine
this question by assuming hypothetical range of the neutrino energy and by
varying the mixing angles and the mass squared differences in the standard
case. We found the cases where Independent Crossing Approximation breaks down
for some unrealistic range of the mass squared difference and the mixing angle.
We also discuss the criterion which gives such independence.
