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We develope in great computational details the classical Cartan equivalenceproblem for Levi-nondegenerate C^6-smooth real hypersurfaces M^3 in C^2,performing all calculations effectively in terms of a (local) graphing function\varphi. In particular, we present explicitly the unique (complex) essentialinvariant J of the problem. Its expansion in terms of the 3-variables function\varphi incorporates millions of differential monomials, while, when \varphi isassumed to depend only on 2 variables (rigid case), J writes out in two lines(7 monomials).

Cartan equivalences for Levi-nondegenerate hypersurfaces M^3 in C^2 belonging to General Class I