  The present paper refers to the knot theory and is devoted to the study of
global properties of Gordian graphs of various local moves. In 2005, Gambaudo
and Ghys raised the question of the behavior at infinity of the crossing change
Gordian graph. They proposed studying its "ends", that is, unbounded connected
components of complements of bounded subsets. We provide a complete description
of the behavior at infinity for local moves from three well-known infinite
families, namely, rational moves, $C(n)$-moves, and $H(n)$-moves (note that
each of the first two families contains the crossing change). Also, in 2005,
March\'e gave a different perspective on the behavior of Gordian graphs at
infinity, proposing to consider complements of finite subsets. We describe the
behavior at infinity in this sense for all local moves with the infinite
neighborhood of the unknot in the corresponding Gordian graph.
