Swapping Equipment Glyphs:
If a Unique Hero you control equipped with an Equipment Glyph stops on another Equipment Glyph, after activating that glyph, you may choose to swap the glyph on that Unique Hero’s card with the glyph it stopped on. Place the Equipment Glyph that Unique Hero previously had equipped power-side up onto a space that Hero currently occupies, and place the Equipment Glyph that was previously on the battlefield onto its card.
You may also swap an Equipment Glyph if a figure you control ends its movement adjacent to another friendly figure equipped with a glyph, as long as both figures can equip both glyphs. Place an Equipment Glyph on the card of the figure you control onto the card of that friendly figure, and vice versa.
Passing Equipment Glyphs:
At any point before, during, or after moving a figure you control equipped with an Equipment Glyph, you may announce that the figure is passing the Equipment Glyph to an adjacent friendly figure that is able to equip it and is not already equipped with a glyph. Place the Equipment Glyph on that friendly figure’s Army Card.
When Swapping glyphs between cards and spaces, you must place the glyph power-side up. However, it doesn't specify this when Swapping or Passing between figures.
When figures Swap and Pass glyphs, may they keep it symbol-side up?
May they turn it symbol-side up when Swapping/Passing if they wanted?
EDIT:
I guess you could theoretically place it face-down, but I don't think you'd really have a mechanic for picking it up, unless you have Bats drop it then pick it back up.
I think you're right, those rules about Passing to/Swapping between figures don't mention anything about turning the glyph.
So, following those rules, if they are symbol side-up, they would remain symbol-side up when passed/swapped between figures.
Dropping Equipment Glyphs:
At any point before, during, or after moving a figure you control equipped with an Equipment Glyph, you may announce that the figure is dropping an Equipment Glyph. Place the Equipment Glyph power-side up onto a space that figure currently occupies. That figure may continue its movement. You cannot drop an Equipment Glyph onto a space that already has another glyph on it.
So in this situation, the order of operations in one turn would follow:
!. End movement adjacent to figure you wish to Swap with.
2. Swap Glyphs, keep them Symbol-Side Up.
3. Drop Glyph Power Side-Up.
4. Re-Equip Glyph.
Or, to cut to the chase, swap e-glyphs, turning the glyph power-side up on only the activated figure's turn.