Matching up the boosts followed by rotations, in the original setup, an observer in Σ notices Σ′′ to move with velocity u ⊕ v then rotate clockwise (first diagram), and because of the rotation an observer in Σ′′ notices Σ to move with velocity − v ⊕ u then rotate anticlockwise (second diagram). If the velocities are exchanged an observer in Σ notices Σ′′ to move with velocity v ⊕ u then rotate anticlockwise (third diagram), and because of the rotation an observer in Σ′′ notices Σ to move with velocity − u ⊕ v then rotate clockwise (fourth diagram).