  On a smooth complete Riemannian spin manifold with smooth compact boundary,
we demonstrate that the Atiyah-Singer Dirac operator $\mathrm{D}_{\mathcal B}$
in $\mathrm{L}^{2}$ depends Riesz continuously on $\mathrm{L}^{\infty}$
perturbations of local boundary conditions ${\mathcal B}$. The Lipschitz bound
for the map ${\mathcal B} \to {\mathrm{D}}_{\mathcal B}(1 +
{\mathrm{D}}_{\mathcal B}^2)^{-\frac{1}{2}}$ depends on Lipschitz smoothness
and ellipticity of ${\mathcal B}$ and bounds on Ricci curvature and its first
derivatives as well as a lower bound on injectivity radius. More generally, we
prove perturbation estimates for functional calculi of elliptic operators on
manifolds with local boundary conditions.
