  The Pancharatnam - Berry phase (PBP) of purely geometric origin appears as a
reparametrization invariant quantity of ray Space. In this article, we
investigate the properties exhibited by PBP in neutrino mixing. We map the
neutrino flavour modes to independent flavour vacuum states and compute PBP
using Bargmann invariant. We derive the exact formula for PBP in two flavour
approximation using the kinematic approach. Our result reproduces previous
results of Blasone et al. under cyclic condition. Inspired by the work of
Mukunda and Simon, we investigate the total and dynamical phases separately.
This method leads us to identify the existence of nodal points in the mixing
parameter space. At nodal points, PBP changes by a value $\pi$, and it
originates from the total phase. We report the direct relation between nodal
points and MSW resonance, giving physical meaning to nodal points. Our analysis
shows the ability of PBP to differentiate between different mass hierarchies
and set numerical bounds to $\Delta m^2$ by changing total energy. We extend
our studies to three flavour model and found that PBP is sensitive to the Dirac
$CP$ phase ($\delta_{CP}$). Using our $N$-qubit architecture of the $N$-flavour
neutrino model, one can immediately study the dynamical characteristics like
mode entanglement between neutrino flavour modes.
