Many are just one sided these days thankfully . But for the two sided ones ... i look at the underside , if its unused i leave it be , if it has marks or looks like its being flipped i do both sides .
ideally you need to dry both sides while you there if you intend to leave it back on the slats . If you cant dry it , i would try and leave it up of them in some way , even fully on its side .
Mattress are heavy to handle but rarley so heavy you cant manhandle them upright in some way .
If you want to dry them while your there you need a strong blower or two . I have a couple of pics on the phone of a recent example ...il find it .