Investigate the covering of the sphereby the sphere associated with the rational function

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Here there is an example of Singerman Complex Functions, i think i understand it, the point is that having $f$ degree 3, do i have three copies of $\mathbb{C}$? if so, how can i glue them?

What i want to know is how to draw the surface $S$ such that $S \to \widehat{\mathbb{C}}$. Thanks

Singerman Complex Functions

Three copies of $\mathbb{C}$