Fuzzy relations and reciprocal relations are two popular tools for representing degrees of preference. It is important to note that they carry a different semantics and cannot be equated directly. We propose a simple transformation based on implication operators that allows to establish a one-to-one correspondence between both formalisms. It sets the basis for a common framework in which properties such as transitivity can be studied and definitions belonging to different formalisms can be compared. As a byproduct, we propose a new family of upper bound functions for cycle-transitivity. Finally, we unveil some interesting equivalences between types of transitivity that were left uncompared till now.