  Let $c,h$ and $c,\tilde{h}$ be two admissible pairs of central charge and
highest weight for ${\rm Diff}^+(S^1)$. It is shown here that the positive
energy irreducible projective unitary representations $U_{c,h}$ and
$U_{c,\tilde{h}}$ of the group ${\rm Diff}^+(S^1)$ are locally equivalent. This
means that for any $I\Subset S^1$ open proper interval, there exists a unitary
operator $W_I$ such that $W_I U_{c,h}(\gamma)W_I^* = U_{c,\tilde{h}}(\gamma)$
for all $\gamma \in {\rm Diff}^+(S^1)$ which act identically on $I^c\equiv
S^1\setminus I$ (i.e. which can "displace" or "move" points only in $I$). This
result extends and completes earlier ones that dealt with only certain regions
of the "$c,h$-plane", and closes the gap in the full classification of
superselection sectors of Virasoro nets.
