  We study precession dynamics of generic binary black holes in eccentric
orbits using an effective potential based formalism derived in [M. Kesden et
al., PRL {\bf 114}, 081103 (2015)]. This effective potential is used to
classify binary black holes into three mutually exclusive spin morphologies.
During the inspiral phase, binaries make transitions from one morphology to
others. We evolve a population of binary black holes from an initial separation
of $1000\mathbf{M}$ to a final separation of $10\mathbf{M}$ using
post-Newtonian accurate evolution equations. We find that, given suitable
initial conditions, a binary's eccentricity can follow one of three distinct
evolutionary patterns: (i) eccentricity monotonically increasing until final
separation, (ii) eccentricity rising after decaying to a minimum value, and
(iii) eccentricity monotonically decreasing throughout the inspiral. The
monotonic growth or growth after reaching a certain minimum of eccentricity is
due to the effect of 2PN spin-spin coupling. Further, we investigate the
morphology transitions in eccentric binaries and find that the probability of
such binaries transiting from one to other is similar to those in circular
orbits, implying that eccentricity plays a sub-dominant role in spin morphology
evolution of a precessing binary black hole. We, hence, argue that the
morphological classification of spin precession dynamics is a robust tool to
constrain the formation channels of binaries with arbitrary eccentricity as
well.
