  We use the formalism of geodesic Witten diagrams to study the holographic
realization of the conformal block expansion for entanglement entropy of two
disjoint intervals. The agreement between the Ryu-Takayanagi formula and the
identity block contribution has a dual realization as the product of bulk to
boundary propagators. Quantum bulk corrections instead arise from stripped
higher order diagrams and back-reaction effects; these are also mapped to the
structure for $G_N^0$ terms found in \cite{Faulkner:2013ana}, with the former
identified as the bulk entanglement entropy across the Ryu-Takayanagi surfaces.
An independent derivation of this last statement is provided by implementing a
twist-line formalism in the bulk, and additional checks from the computation of
mutual information and single interval entanglement entropy. Finally an
interesting correspondence is found between the recently proposed holographic
entanglement of purification, and an approximated form for certain $1/c$ Renyi
entropies corrections.
