  We propose a framework for the specification of behaviour-preserving
reconfigurations of systems modelled as Petri nets. The framework is based on
open nets, a mild generalisation of ordinary Place/Transition nets suited to
model open systems which might interact with the surrounding environment and
endowed with a colimit-based composition operation. We show that natural
notions of bisimilarity over open nets are congruences with respect to the
composition operation. The considered behavioural equivalences differ for the
choice of the observations, which can be single firings or parallel steps.
Additionally, we consider weak forms of such equivalences, arising in the
presence of unobservable actions. We also provide an up-to technique for
facilitating bisimilarity proofs. The theory is used to identify suitable
classes of reconfiguration rules (in the double-pushout approach to rewriting)
whose application preserves the observational semantics of the net.
