  We develop a strategy to classify the components of the space of sections of
a del Pezzo fibration over $\mathbb{P}^{1}$. In particular, we prove the
Movable Bend and Break lemma for del Pezzo fibrations. Our approach is
motivated by Geometric Manin's Conjecture and proves upper bounds on the
associated counting function. We also give applications to enumerativity of
Gromov-Witten invariants and to the study of the Abel-Jacobi map.
