  Recent data from p+p and p+Pb collisions at the Large Hadron Collider (LHC),
and d+Au and $^3$He+Au collisions at the Relativistic Heavy Ion Collider (RHIC)
reveal patterns that---when observed in the collision of heavy nuclei---are
commonly interpreted as indicators of a locally equilibrated system in
collective motion. The comparison of these data sets, including the forthcoming
results from p+Au and p+Al collisions at RHIC, will help to elucidate the
geometric dependence of such patterns. It has recently been shown that
A-Multi-Phase-Transport-Model (AMPT) can describe some of these features in LHC
data with a parton-parton scattering cross section comparable to that required
to describe A+A data. In this paper, we extend these studies by incorporating a
full wave function description of the $^3$He nucleus to calculate elliptical
and triangular anisotropy moments $v_2$ and $v_3$ for p+Au, d+Au and $^3$He+Au
collisions at the RHIC top energy of 200 GeV. We find reasonable agreement with
the measured $v_2$ in d+Au and $^3$He+Au and $v_3$ in $^3$He+Au for transverse
momentum ($p_{T}$) $\lesssim$ 1 GeV/c, but underestimate these measurements for
higher values of \pt. We predict a pattern of coefficients ($v_{2}$, $v_{3}$)
for \pau, dominated by differences in the number of induced local hot spots
(i.e. one, two, or three) arising from intrinsic geometry. Additionally, we
examine how this substantial azimuthal anisotropy accrues during each
individual evolutionary phase of the collision in the AMPT model. The
possibility of a simultaneous description of RHIC- and LHC-energy data, the
suite of different geometries, and high multiplicity p+p data is an exciting
possibility for understanding the underlying physics in these systems.
