Non-displaceable Lagrangian links in four-manifolds

Let $omega$ denote an area form on $S^2$. Consider the closed symplectic 4-manifold $M=(S^2times S^2, Aomega oplus a omega)$ with $0<a<A$. We show that there are families of displaceable Lagrangian tori $L_{0,x},, L_{1,x} subset M$, for $x in [0,1]$, such that the two-component link $L_{0,x} cup L_{1,x}$ is non-displaceable for each $x$.