Motivated by Berkovich's nine $q$-binomial identities involving the Legendre symbol $(\frac{d}{3})$, we establish a unified form of $q$-binomial identities of this type through a combinatorial approach. This unified form includes Berkovich's nine identities as special cases. Many such identities can be also deduced from this unified form.
A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers
The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons
Proofs of some binomial identities using the method of last squares
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