  Given a semi-Markov law, using an additional parameter, we consider a family
of stochastic flows corresponding to that law. Then we suitably select a
particular flow, for which we obtain expressions of the meeting and merging
probabilities of a pair of semi-Markov processes, solving the same equation but
having two different initial conditions. A set of sufficient conditions are
also obtained under which any two solutions of the flow eventually merge with
probability one.
