A transept shown on a typical cathedral plan
The crossing belongs to both transept and nave
A transept is, in Romanesque and Gothic church architecture, an area set across the nave in a cruciform building. The transept separates the nave from the sanctuary.
The point where to main axis crosses the transept, known simply as the crossing, belongs to both the nave and the transept.
Depending on the size of the building, the arms of the transept may have one chapel each, or several chapels.
When speaking of the left and right arms of the transept, the view is always from the entrance towards the sanctuary.