A reducibility in the theory of iterative combinatory spaces

The notion of iterative combinatory space introduced in the past by the present author gave the framework for an algebraic generalization of a part of Computability Theory. In the present paper a reducibility concerning iterative combinatory spaces is considered, as well as the corresponding equivalence. A statement of J.~Zashev about variants of iterative combinatory spaces is shown to fail under certain interpretations of the notion of variant in the terms of the relations in question.