  The aim of this article is to make a first step towards the classification of
complex normal affine $\mathbb G_a$-threefolds $X$. We consider the case where
the restriction of the quotient morphism $\pi\colon X\to S$ to $\pi^{-1}(S_*)$,
where $S_*$ denotes the complement of some regular closed point in $S$, is a
principal $\mathbb G_a$-bundle. The variety $\mathrm{SL}_2$ will be of special
interest and a source of many examples. It has a natural right $\mathbb
G_a$-action such that the quotient morphism $\mathrm{SL}_2\to\mathbb A^2$
restricts to a principal $\mathbb G_a$-bundle over the punctured plane $\mathbb
A^2_*$.
