Given a plane graph $G$, consider a subgraph $H$. If $H$ contains a leaf $l$ (an edge in which at least one endpoint $v$ is not part of any other edge) which is not a leaf in $G$, define a spin of $l$ as the new subgraph $H'\subset G$ obtained from $H \setminus l$ by adding one edge of $G$ that has $v$ as one of its endpoints.
Is this operation known and studied? I am particularly interested in equivalence classes of subgraphs under this spinning operation. As an example, are all spanning trees in a given plane and $2$-connected graph related by a finite sequence of such leaf spins?
I've been given this reference which answers positively the last question, namely that all spanning trees are related by finite applications of leaf spins: "The Connectivities of Leaf Graphs of 2-Connected Graphs, Journal of Combinatorial Theory, Series B 76, 155169 (1999)".