  Using the notion of series parallel interval order, we propose a unified
setting to describe Dyck lattices and Tamari lattices (two well known lattice
structures on Catalan objects) in terms of basic notions of the theory of
posets. As a consequence of our approach, we find an extremely simple proof of
the fact that the Dyck order is a refinement of the Tamari one. Moreover, we
provide a description of both the weak and the strong Bruhat order on
312-avoiding permutations, by recovering the proof of the fact that they are
isomorphic to the Tamari and the Dyck order, respectively; our proof, which
simplifies the existing ones, relies on our results on series parallel interval
orders.
