  The (3+1)-dimensional Dirac equation with position dependent mass in 4-vector
electromagnetic fields is considered. Using two over-simplified examples (the
Dirac-Coulomb and Dirac-oscillator fields), we report energy-levels crossing as
a spectral property or as an effect of the hidden supersymmetric quantum
mechanical language and/or quasi-parity signatures. Under different settings of
the related interactions' way-of-coupling into Dirac equation, it is observed
that the two ultimate/effective descendents, Dirac-Coulomb and
Dirac-oscillator, exhibit different conditions on the energy-levels crossings.
