jats:titleAbstract</jats:title>jats:pWe discuss the symplectic topology of the Stein manifolds obtained by plumbing two 3-dimensional spheres along a circle. These spaces are related, at a derived level and working in a characteristic determined by the specific geometry, to local threefolds which contain two floppablejats:inline-formulajats:alternativesjats:tex-math$$(-1,-1)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">mml:mrowmml:mo(</mml:mo>mml:mo-</mml:mo>mml:mn1</mml:mn>mml:mo,</mml:mo>mml:mo-</mml:mo>mml:mn1</mml:mn>mml:mo)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>-curves meeting at a point. Using contraction algebras we classify spherical objects on the B-side, and derive topological consequences including a complete description of the homology classes realised by graded exact Lagrangians.</jats:p>