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Let $C,D$ be two non-compact complex algebraic smooth curves. Suppose that two unramified regular finite maps $p_1, p_2: C \rightarrow D$ are given. Is there always an automorphism $\varphi:C \rightarrow C$ such that $p_1=p_2\circ \varphi$?

Let $C,D$ be two non-compact complex algebraic smooth curves. Suppose that two unramified regular finite maps $p_1, p_2: C \rightarrow D$ are given and have the same degree. Is there always an automorphism $\varphi:C \rightarrow C$ such that $p_1=p_2\circ \varphi$?

Let us consider two unramified covers $p_1, p_2: C \rightarrow D$ between affine Riemann surfaces. Is there always an automorphism $\varphi:C \rightarrow C$ such that $p_1=p_2\circ \varphi$?

Let $C,D$ be two non-compact complex algebraic smooth curves. Suppose that two unramified regular finite maps $p_1, p_2: C \rightarrow D$ are given. Is there always an automorphism $\varphi:C \rightarrow C$ such that $p_1=p_2\circ \varphi$?