Overtwisted = Tight in 3 dimensions

We prove the equivalence of Eliashberg overtwisted $h$—principle and  the Eliashberg-Mishachev classification of contact structures in the tight $3$-ball. I.e. we prove that simple algebraic topology computations takes us from one result to the other. We will hint what can be proven in higher dimensions and we left the careful listener with the task of extracting the corollaries of this result.