  The dark energy transition between quintessence ($w>-1$) and phantom ($w<-1$)
regimes (the crossing of the cosmological constant boundary) is studied using
the dark energy equation of state. Models characterized by this type of
transition are explicitly constructed and their equation of state is found to
be {\em implicitly} defined. The behavior of the more general models with the
implicitly defined equation of state, obtained by the generalization of the
explicitly constructed models, is studied to gain insight into the necessary
conditions for the occurrence of the transition, as well as to investigate the
mechanism behind the transition. It is found that the parameters of the
generalized models need to satisfy special conditions for the transition to
happen and that the mechanism behind the transition is the cancellation of the
contribution of the cosmological constant boundary. The aspects of the behavior
of the generalized models which are not related to the transition are briefly
discussed and the role of the implicitly defined dark energy equation of state
in the description of the dark energy evolution is emphasized.
