  Reactive systems (RSs) represent a meta-framework aimed at deriving
behavioral congruences for those computational formalisms whose operational
semantics is provided by reduction rules. RSs proved a flexible specification
device, yet so far most of the efforts dealing with their behavioural semantics
focused on idem pushouts (IPOs) and saturated (also known as dynamic)
bisimulations. In this paper we introduce a novel, intermediate behavioural
equivalence: L-bisimilarity, which is able to recast both its IPO and saturated
counterparts. The equivalence is parametric with respect to a set L of RSs
labels, and it is shown that under mild conditions on L it is indeed a
congruence. Furthermore, L-bisimilarity can also recast the notion of barbed
semantics for RSs, proposed by the same authors in a previous paper. In order
to provide a suitable test-bed, we instantiate our proposal by addressing the
semantics of (asynchronous) CCS and of the calculus of mobile ambients.
