The yeast is stored under sterile distilled water in the jars . . . which is an excellent method for long term storage, as can be see from the dates on some of those Jars
. When I want to use the yeast, I shake to suspend the yeast in the vial, then heat a platinum loop in a flame until glowing, remove the lid of the vial, flaming the neck then working in the 'zone of the flame' I transfer a loopful to another vial containing sterile wort. this is then sealed and left in a warm place to get going . . Step up to 20ml once its working (24-36 hours), then to 200ml, then to 2L. If I want to ensure its viable, I will plate it on a wort agar plate in a petri dish, and select a colony to use after 3 days.
Long term viability is probably around 10 years or so, storing slurry under wort or distilled water is limited to around 6 months, but because the amount of yeast is so small and the qty of water is so big (And there are no nutrients in the water) then the yeast go into suspended animation until the conditions improve.
When I buy a new Yeast variety, the tube is tipped into a 5L starter and I remove a loopful from dregs of the tube and store it in the distilled water . .. that becomes my primary source, and I'm always working from the original generation of yeast.
The method does involve the knowledge of sterile transfer techniques and how to produce sterile containers (Sterile not sanitised!), but for maintaining a working yeast collection long term it is invaluble
Other techniques for yeast storage are available, this is not meant as a criticism of any other method 
