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We give constructions of completions of the affine $3$-space into totalspaces of del Pezzo fibrations of every degree other than $7$ over theprojective line. We show in particular that every del Pezzo surface other than$\mathbb{P}^{2}$ blown-up in one or two points can appear as a closed fiber ofa del Pezzo fibration $\pi:X\to\mathbb{P}^{1}$ whose total space $X$ is a$\mathbb{Q}$-factorial threefold with terminal singularities which contains$\mathbb{A}^{3}$ as the complement of the union of a closed fiber of $\pi$ anda prime divisor $B_{h}$ horizontal for $\pi$. For such completions, we alsogive a complete description of integral curves that can appear as generalfibers of the induced morphism $\bar{\pi}:B_{h}\to\mathbb{P}^{1}$.

Completions of the affine $3$-space into del Pezzo fibrations