  A temporal graph is a graph whose edges only appear at certain points in
time. Reachability in these graphs is defined in terms of paths that traverse
the edges in chronological order (temporal paths). This form of reachability is
neither symmetric nor transitive, the latter having important consequences on
the computational complexity of even basic questions, such as computing
temporal connected components. In this paper, we introduce several parameters
that capture how far a temporal graph $\mathcal{G}$ is from being transitive,
namely, \emph{vertex-deletion distance to transitivity} and
\emph{arc-modification distance to transitivity}, both being applied to the
reachability graph of $\mathcal{G}$. We illustrate the impact of these
parameters on the temporal connected component problem, obtaining several
tractability results in terms of fixed-parameter tractability and polynomial
kernels. Significantly, these results are obtained without restrictions of the
underlying graph, the snapshots, or the lifetime of the input graph. As such,
our results isolate the impact of non-transitivity and confirm the key role
that it plays in the hardness of temporal graph problems.
