  This note extends and strengthens a theorem of Bates that says that
row-finite graphs that are strong shift equivalent have Morita equivalent graph
C*-algebras. This allows us to ask whether our stronger notion of Morita
equivalence does in fact characterise strong shift equivalence. We believe this
will be relevant for future research on infinite graphs and their C*-algebras.
We also study insplits and outsplits as particular examples of strong shift
equivalences and show that the induced Morita equivalences respect a whole
family of weighted gauge actions. We then ask whether strong shift equivalence
is generated by (generalised) insplits and outsplits.
