Tried it both ways, subject to change, but air's my current go-to method.
If that 13mm dead space works out to .15ml, and I'm mixing at 30mg per ml, that's roughly 4.5mg sitting in the filter, or about a dollar's worth of reta wasted.
Here's another angle worth considering:
Sixty milligrams of reta, total diluent comes to 2ml to land on that same 30mg/ml concentration. Draw 1ml for the initial mix, send that through the filter, then flush the original vial using the remaining diluent along with that leftover dead-space amount. Whatever peptide's left in that flush is minimal, so no need to worry about purging it out.
This really only matters more once you're working with bigger vials or pricier peptides, like the higher-strength tirz or reta options, or compounds running several times the cost per milligram.
Needles run about a dime each, a barrel's roughly fifteen cents, and a filter's about half a dollar. Doing the flush method eats up a single filter, a pair of barrels, and four needles altogether, one each for venting, filtering, mixing, and flushing. All told, that lands just over a dollar in supplies.