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We study the equivariant disc potentials for immersed SYZ fibers in toricCalabi-Yau manifolds. The immersed Lagrangians play a crucial role in thepartial compactification of the SYZ mirrors. Morever, their equivariant discpotentials have a close relation with that of Aganagic-Vafa branes. We showthat the potentials can be computed by using an equivariant version ofisomorphisms in the Fukaya category.

$T$-equivariant disc potentials for toric Calabi-Yau manifolds