Two meromorphic functions sharing some pairs of values on an annuli

In this paper, we will prove that two admissible meromorphic functions on an annuli sharing \(q\ (q \ge 6)\) $q(q\ge 6)$ pairs of values in \({\mathbb {C}}\cup \{\infty \}\) $\mathbb{C}\cup \{\infty \}$ with different multiple values are linked by a Möbius transformation.