  We provide a novel proof that the set of directions that admit a saddle
connection on a meromorphic quadratic differential with at least one pole of
order at least two is closed, which generalizes a result of Bridgeland and
Smith, and Gaiotto, Moore, and Neitzke. Secondly, we show that this set has
finite Cantor-Bendixson rank and give a tight bound. Finally, we present a
family of surfaces realizing all possible Cantor-Bendixson ranks. The
techniques in the proof of this result exclusively concern Abelian
differentials on Riemann surfaces, also known as translation surfaces. The
concept of a "slit translation surface" is introduced as the primary tool for
studying meromorphic quadratic differentials with higher order poles.
