  Flip graphs of combinatorial and geometric objects are at the heart of many
deep structural insights and connections between different branches of discrete
mathematics and computer science. They also provide a natural framework for the
study of reconfiguration problems. We study flip graphs of arrangements of
pseudolines and of arrangements of pseudocircles, which are combinatorial
generalizations of lines and circles, respectively. In both cases we consider
triangle flips as local transformation and prove conjectures regarding their
connectivity.
  In the case of $n$ pseudolines we show that the connectivity of the flip
graph equals its minimum degree, which is exactly $n-2$. For the proof we
introduce the class of shellable line arrangements, which serve as reference
objects for the construction of disjoint paths. In fact, shellable arrangements
are elements of a flip graph of line arrangements which are vertices of a
polytope (Felsner and Ziegler; DM 241 (2001), 301--312). This polytope forms a
cluster of good connectivity in the flip graph of pseudolines. In the case of
pseudocircles we show that triangle flips induce a connected flip graph on
\emph{intersecting} arrangements and also on cylindrical intersecting
arrangements. The result for cylindrical arrangements is used in the proof for
intersecting arrangements. We also show that in both settings the diameter of
the flip graph is in $\Theta(n^3)$. Our constructions make essential use of
variants of the sweeping lemma for pseudocircle arrangements (Snoeyink and
Hershberger; Proc.\ SoCG 1989: 354--363). We finally study cylindrical
arrangements in their own right and provide new combinatorial characterizations
of this class.
