  We introduce a new distance dist_oq between compact quantum metric spaces. We
show that dist_oq is Lipschitz equivalent to Rieffel's distance dist_q, and
give criteria for when a parameterized family of compact quantum metric spaces
is continuous with respect to dist_oq. As applications, we show that the
continuity of a parameterized family of quantum metric spaces induced by
ergodic actions of a fixed compact group is determined by the multiplicities of
the actions, generalizing Rieffel's work on noncommutative tori and integral
coadjoint orbits of semisimple compact connected Lie groups; we also show that
the theta-deformations of Connes and Landi are continuous in the parameter
theta.
