This article designs a general principle to check the correctness of the definition of concurrency (a.k.a. independence) of events for concurrent calculi. Concurrency relations are central in process algebras, but also two-sided: they are often defined independently on composable and on coinitial transitions, and no criteria exists to assess whether they "interact correctly". This article starts by examining how reversibility can provide such a correctness of concurrencies criteria, and its implications. It then defines, for the first time, a syntactical definition of concurrency for CCSK, a reversible declension of the calculus of communicating systems. To do so, according to our criteria, requires to define concurrency relations for all types of transitions along two axis: direction (forward or backward) and concomitance (coinitial or composable). Our definition is uniform thanks to proved transition systems and satisfy our sanity checks: square properties, sideways diamonds, but also the reversible checks (reverse diamonds and causal consistency). We also prove that our formalism is either equivalent to or a refinement of pre-existing definitions of concurrency for reversible systems. We conclude by discussing additional criteria and possible future works.