I am having a trouble in understanding the Example 4.7 (pages 65-66), the genus two fibrations with $p_g=0$, $q=1$, and $K^2 = -3$, in "Surfaces fibrées en courbes de genre deux", Lecture Notes in Mathematics, 1137. My French is not good and the Google translator confused me even more. If you are familiar with this construction, could you please outline it?

Especially, I don't understand how the branch divisor $D$ is defined on page 66. Also, does it follow from the construction that the fibration admits $-1$ sphere section? Thanks in advance.