Pierced pothole can not be considers like a natural bridge. Most of the pierced pothole are located on the side of the canyon wall or on the main drainage but its do not spans the whole canyon. Generaly, it is little in size (about 1 or 3  meters diameter maximum). For these reasons, its should be called "natural arch" though it was formed by water flow.

Potholes of Peek-A-Boo (USA)

Potholes of Peonera (Spain)

Potholes of Vero (Spain)

Marmites Percées de la Valserine (France)

Pothole of Aiglun (France)