  We prove that the cardinality of transitive quasi-uniformities in a
quasi-proximity class is at least $2^{2^{\aleph_0}}$ if there exist at least
two transitive quasi-uniformities in the class. The transitive elements of
$\pi(\delta)$ are characterized if ${\cal V}_{\delta}$ is transitive, and in
this case we give a condition when there exists a unique transitive
quasi-uniformity in $\pi(\delta)$.
