An elliptic incarnation of the Bailey chain

For the first time a Bailey chain with all entries composed out of the Jacobi theta functions is constructed. This is an elliptic extension of the WP (well-poised) Bailey chain of Andrews and it generates an infinite sequence of identities for theta hypergeometric series. As a particular example, we obtained a new proof of the Frenkel-Turaev elliptic analogue of the Bailey transformation for a terminating 10Φ9 basic hypergeometric series. An elliptic generalization of the Andrews-Berkovich 10Φ9 → 12Φ11 transformation formula is derived by employing an elliptic extension of a Bressoud's Bailey pair.