The last distribution-equivalence class of mesh patterns of length 2

We prove the remaining conjectural distribution-equivalence of mesh patterns of length 2 from 2019. This completes the classification of distribution-equivalence and Wilf-equivalence classes for mesh patterns of length 2. Consequently the numbers of such classes are 105 and 46, respectively. We approach this by constructing a marked occurrence bijection, in the spirit of the cluster method for consecutive patterns.