  We propose and recursively prove polynomial identities which imply
Capparelli's partition theorems. We also find perfect companions to the results
of Andrews, and Alladi, Andrews and Gordon involving $q$-trinomial
coefficients. We follow Kur\c{s}ung\"oz's ideas to provide direct combinatorial
interpretations of some of our expressions. We use of the trinomial analogue of
Bailey's lemma to derive new identities. These identities relate triple sums
and products. A couple of new Slater type identities are also noted.
