It is well known that interleaving presentations is at the heart of fibring, as shown by the mechanism of fibring languages and deduction systems. This idea is abstractly introduced at the level of a suitably general notion of graph. Such graphs are used to present languages, interpretation structures and deduction systems in a uniform way. The induced semantics of fibring is very simple and avoids the collapsing problem. Transference results are also easier to establish. Joint work with A. Sernadas, J. Rasga and M. Coniglio.