  We consider a time varying analogue of the Erd{\H o}s-R{\' e}nyi graph and
study the topological variations of its associated clique complex. The dynamics
of the graph are stationary and are determined by the edges, which evolve
independently as continuous time Markov chains. Our main result is that when
the edge inclusion probability is of the form $p = n^\alpha$, where $n$ is the
number of vertices and $\alpha \in (-1/k, -1/(k + 1)),$ then the process of the
normalized $k-$th Betti number of these dynamic clique complexes converges
weakly to the Ornstein-Uhlenbeck process as $n \to \infty.$
