You would want to store them partly or mostly filled with dry air. Moist air can possibly start a moldy condition. You could store them with open valve, but then you have little control over the air quality. You probably would not want to store them tightly inflated, because that might possibly lead to a leak. OTOH, if you did store them inflated, and then if you checked on them later and found it to be only partly inflated, you would know that a leak had been developed. It would be better to discover those things at home and not out on the trail.