  We present the formulae for twist quantization of $g_2$, corresponding to the
solution of classical YB equation with support in the 8-dimensional Borel
subalgebra of $g_2$. The considered chain of twists consists of the four
factors describing the four steps of quantization: Jordanian twist, the two
twist factors extending Jordanian twist and the deformed Jordanian or in second
variant additional Abelian twist. The first two steps describe as well the
$sl(3)$ quantization. The coproducts are calculated for each step in explicite
form, and for that purpose we present new formulas for the calculation of
similarity transformations on tensor product. We introduce new basic generators
in universal enveloping algebra $U(g_2)$ which provide nonlinearities in
algebraic sector maximally simplifying the deformed coproducts.
