The first way of reading the pairs that came to mind for me was placing both of the input atoms on the same unification glyph. In order for the two atoms to disappear if they were different, I need to compare them to their complimentary pair.  I can't know which one that is, so I have to check all of them.

I started writing down the different combinations of atoms in a notebook, taking into account their orientation on the glyph doesn't matter.  Afterwards, I went into Tabletop Simulator and opened up the opus magnum workshop mod that has tiles of all the different atoms and got to work. Fiddling with them, I lined up the cases vertically and noticed that I could squish some cases together if I used a hexarm.  The only one that didn't fit was the Earth/Water pair, which I was able to fit in by scooting the atoms around with a second hexarm because of the order of atoms I happened to pick.