The OP referred to his hitch as an "equalizer" but if it truly is an Equal-i-zer brand hitch then another potential issue is the head angle may have to be changed when switching from one vehicle to the other. Anyone who owns an Equal-i-zer knows this is a real PITA as it means pulling the head apart and changing the number of washers in the head, which in turn means having a torque wrench on hand that will properly torque those two shank bolts. :( Perhaps the OP could be more specific and tell us just which hitch he really has. ;)