  Both hydrodynamics-based models and a multi-phase transport (AMPT) model can
reproduce the mass splitting of azimuthal anisotropy ($v_n$) at low transverse
momentum ($p_{\perp}$) as observed in heavy ion collisions. In the AMPT model,
however, $v_n$ is mainly generated by the parton escape mechanism, not by the
hydrodynamic flow. In this study we provide detailed results on the mass
splitting of $v_n$ in this transport model, including $v_2$ and $v_3$ of
various hadron species in d+Au and Au+Au collisions at the Relativistic Heavy
Ion Collider and p+Pb collisions at the Large Hadron Collider. We show that the
mass splitting of hadron $v_2$ and $v_3$ in AMPT first arises from the
kinematics in the quark coalescence hadronization process, and then, more
dominantly, comes from hadronic rescatterings, even though the contribution
from the latter to the overall charged hadron $v_n$ is small. We further show
that there is no qualitative difference between heavy ion collisions and
small-system collisions or between elliptic ($v_2$) and triangular ($v_3$)
anisotropies. Our studies thus demonstrate that the mass splitting of $v_2$ and
$v_3$ at low-$p_{\perp}$ is not a unique signature of hydrodynamic collective
flow but can be the interplay of several physics effects.
