A multi-section screen system includes a first of the flexible sheets of screen material that has zipper teeth along at least one side edge and a neighboring second flexible sheet of screen material that has mating zipper teeth along an abutting side edge. Mechanisms retract and deploy each of the flexible sheets in unison. A fastener is fixedly disposed between each two of the mechanisms. The fasteners automatically join the zipper teeth with the mating zipper teeth as the mechanisms deploy the flexible sheets and the fasteners automatically disengaging the zipper teeth from the mating zipper teeth as the mechanisms retract the flexible sheets.