Mirror symmetry is related to the existence of two different strata of the boundary $\partial\overline{{\cal M}}^{N=2}$ which we called A-stratum and B-stratum. As a corollary, same quantities admit different geometric descriptions near different strata. In the traditional picture, one can introduce natural coordinates in a small neighborhood of a boundary point corresponding to $(X,J_{X},{{\bf R}}_{+}^{\ast}\cdot g_{X},B)$. Skipping $X$ from the notation, one can say that the coordinates are $(J,g,B)$ (complex structure, Calabi-Yau metric and the B-field). Geometrically, the pairs $(g,B)$ belong to the preimage of the Kähler cone under the natural map $Re:H^{2}(X,{{\bf C}})\to H^{2}(X,{{\bf R}})$ (more precisely, one should consider $B$ as an element of $H^{2}(X,i{{\bf R}}/{{\bf Z}})$). It is usually said, that one considers an open domain in the complexified Kähler cone with the property that with the class of metric $[g]$ it contains also the ray $t[g],t\gg 1$. The mirror symmetry gives rise to an identification of neighborhoods of $(X,J_{X},{{\bf R}}_{+}^{\ast}\cdot g_{X},B_{X})$ and $(X^{\vee},J_{X^{\vee}},{{\bf R}}_{+}^{\ast}\cdot g_{X^{\vee}},B_{X^{\vee}})$ such that $J_{X}$ is interchanged with $[g_{X^{\vee}}]+iB_{X^{\vee}})$ and vice versa.

We can describe this picture in a different way. Using the identification of complex and Kähler moduli, one can choose $([g_{X}],B_{X},[g_{X^{\vee}}],B_{X^{\vee}})$ as local coordinates near the meeting point of A-stratum and B-stratum. There is an action of the additive semigroup ${{\bf R}}_{\geq 0}\times{{\bf R}}_{\geq 0}$ in this neighborhood. It is given explicitly by the formula $([g_{X}],B_{X},[g_{X^{\vee}}],B_{X^{\vee}})\mapsto(e^{t_{1}}[g_{X}],B_{X},e^{t_{2}}[g_{X^{\vee}}],B_{X^{\vee}})$ where $(t_{1},t_{2})\in{{\bf R}}_{\geq 0}\times{{\bf R}}_{\geq 0}$. As $t_{1}\to+\infty$, a point of the moduli space approaches the B-stratum, where the metric is defined up to a positive scalar only. The action of the second semigroup ${{\bf R}}_{\geq 0}$ extends by continuity to the non-trivial action on the B-stratum. Similarly, in the limit $t_{2}\to+\infty$ the flow retracts the point to the A-stratum.

This picture should be modified, if one makes a real blow-up at the corner, as discussed before. Again, the action of the semigroup ${{\bf R}}_{\geq 0}\times{{\bf R}}_{\geq 0}$ extends continuously to the boundary. Contractions to A-stratum and B-stratum carry non-trivial actions of the corresponding semigroups isomorphic to ${{\bf R}}_{\geq 0}$. Now, let us choose a point in, say, A-stratum. Then the semigroup flow takes it along the boundary to the new stratum, corresponding to the double collapse. The semigroup ${{\bf R}}_{\geq 0}\times{{\bf R}}_{\geq 0}$ acts trivially on this stratum. A point of the double collapse is also a limiting point of a $1$-dimensional orbit of ${{\bf R}}_{\geq 0}\times{{\bf R}}_{\geq 0}$ acting on the T-stratum. Explicitly, the element $(t_{1},t_{2})$ changes the size of the tori defined by the Narain lattices, rescaling them with the coefficient $e^{t_{1}-t_{2}}$. This flow carries the point of T-stratum to another point of the double collapse, which can be moved then inside of the B-stratum. The whole path, which is the intersection of $\partial\overline{\cal M}^{N=2}$ and the ${{\bf R}}_{\geq 0}\times{{\bf R}}_{\geq 0}$-orbit, connects an A-model with the corresponding B-model through the stratum of toroidal models. We can depict it as follows:

The T-portion of the path (we call it T-path) connects dual torus fibrations over the same Riemannian base. This is mirror symmetry in our picture.

This description is inspired by [SYZ]. The reader notices however, that in our picture, the mirror symmetry phenomenon is explained entirely in terms of the boundary of the compactified moduli space. In order to explain the mirror symmetry phenomenon it is not necessary to build full SCFTs. It is sufficient to work with simple toroidal models on the boundary of the compactified moduli space $\overline{{\cal M}}^{N=2}$. Also, in contrast with [SYZ], we do not use supersymmetric cycles (D-branes) in our description.