Primitive sets of numbers being equivalent by Frobenius

Equivalence of primitive sets of natural numbers is investigated in connection with the Diophantine Frobenius problem. The equivalence is used for simplifying calculations of Frobenius number $g(a_1,\dots,a_k)$ and of the whole set of numbers that are not contained in the additive semigroup generated by a set $\{a_1,\dots,a_k\}$.