  The author studied in \cite{shi} the covering map property of the local
homeomorphism associating to the space of stability conditions over the
$n$-Kronecker quiver. In this paper, we discuss the covering map property for
stability conditions over the Dynkin quiver of type $A_3$. The local
homeomorphism from a connected component of stability conditions over $A_3$ to
3-dimensional complex vector space becomes a covering map when we restrict it
to the complement of six codimension one subspaces.
