  We study the relativistic accretion flow around a generic stationary
axisymmetric space-time and obtain an effective potential ($\Phi^{\rm eff}$)
that accurately mimics the general relativistic features of Kerr black hole
having spin $0\le a_k <1$. Considering the accretion disc confined around the
equatorial plane of a rotating black hole and using the relativistic equation
of state, we examine the properties of the relativistic accretion flow and
compare it with the same obtained form semi-relativistic as well as
non-relativistic accretion flows. Towards this, we first investigate the
transonic properties of the accretion flow around the rotating black hole where
good agreement is observed for relativistic and semi-relativistic flows.
Further, we study the non-linearities such as shock waves in accretion flow.
Here also we find that the shock properties are in agreement for both
relativistic and semi-relativistic flows irrespective of the black hole spin
($a_k$), although it deviates significantly for non-relativistic flow. In fact,
when the particular shocked solutions are compared for flows with identical
outer boundary conditions, the positions of shock transition in relativistic
and semi-relativistic flows agree well with deviation of $6-12\%$ for $0 \le
a_k \le 0.99$, but vast disagreement is observed for non-relativistic flow. In
addition, we compare the parameter space for shock to establish the fact that
relativistic as well as semi-relativistic accretion flow dynamics do show close
agreement irrespective of $a_k$ values, whereas non-relativistic flow fails to
do so. With these findings, we point out that semi-relativistic flow including
$\Phi^{\rm eff}$ satisfactorily mimics the relativistic accretion flows around
Kerr black hole. Finally, we discuss the possible implications of this work in
the context of dissipative advective accretion flow around Kerr black holes.
