It seems to be set up for a '54 to 56 pass car. So the action to the center carb comes from cross link at the back of the manifold which must pull the bottom hole of the pass side lever towards the back of the car. On the driver's side the lever on the center carb. shaft with the sliding link rotates forward, eventually contacting the stop on the rod to the rear carb. This pulls the back lever and that rotates both rear and front carb shafts together. So I think this set up will rotate all three throttle shafts in a progressive fashion.The front carb is interesting, it seems to have no idle screws or vacuum signal for the dist. With my3/2 setup I kept the front and rear idle screws adjusted out about 1/4 turn so that the air leakage passed the throttle plates had at least some fuel in it. The builder has plugged the vacuum signal port on the center carb.
BTW the levers on the front and back carb must be exactly parallel and positioned properly. The link between them must be exactly the same effective length as the centerline distance between the carbs. The center lever must be longer than the two end levers and the sliding stop on the link to the rear carb provides the progressive action. Most of the time you are driving on the center carb and the rear two don't come into it because the stop has not pulled on the sliding link opening the front and back carbs. Also that set has the acceleration pump links installed on the front and back so there might be too much fuel dumped if it is stomped on.
Don't forget to get the vacuum signal for your distributor from the manifold, those carbs are intended for a Loadomatic dist.