This is a disc with 5 holes.

There up to homeomorphism 2 types of essential closed simple curve. Therefore, up to conjugacy in the mapping class group 2 classes of Dehn twist.

Each ellipse separates the surface into a pantalon and a disc with 4 holes.

The red arc is the Dehn twist of the blue arc round the blue ellipse.

The orange arc is the Dehn twist of the red arc round the red ellipse.

The green arc is the Dehn twist of the orange arc round the orange ellipse.

The blue arc is the Dehn twist of the green arc round the green ellipse.....

Each ellipse separates the surface into a pantalon and a disc with 3 holes.

The red arc is the Dehn twist of the blue arc round the blue ellipse.

The blue arc is the Dehn twist of the red arc round the green ellipse....