  For a quiver with non-degenerate potential, we study the associated stability
scattering diagram and how it changes under mutations. We show that under
mutations the stability scattering diagram behaves like the cluster scattering
diagram associated to the same quiver, which gives them identical cluster
chamber structures. As an application, we prove if the quiver has a
green-to-red sequence, these two scattering diagrams are identical and if the
quiver comes from a once-punctured torus, they differ by a central
wall-crossing. This verifies in those cases a conjecture of
Kontsevich-Soibelman that a particular set of initial data given by a quiver
determines the Donaldson-Thomas series of the quiver with a non-degenerate
potential.
