  The simplicial framework of Engle-Pereira-Rovelli-Livine spin-foam models is
generalized to match the diffeomorphism invariant framework of loop quantum
gravity. The simplicial spin-foams are generalized to arbitrary linear 2-cell
spin-foams. The resulting framework admits all the spin-network states of loop
quantum gravity, not only those defined by triangulations (or cubulations). In
particular the notion of embedded spin-foam we use allows to consider knotting
or linking spin-foam histories. Also the main tools as the vertex structure and
the vertex amplitude are naturally generalized to arbitrary valency case. The
correspondence between all the SU(2) intertwiners and the SU(2)$\times$SU(2)
EPRL intertwiners is proved to be 1-1 in the case of the Barbero-Immirzi
parameter $|\gamma|\ge 1$, unless the co-domain of the EPRL map is trivial and
the domain is non-trivial.
