We study the transition form factors of the light mesons in the kinematics, where one photon is real and other is virtual. Using the dispersive approach to axial anomaly we show that the axial anomaly in this case reveals itself as a collective effect of meson spectrum. This allows us to get the relation between possible corrections to continuum and to lower states within QCD method which does not rely on factorization hypothesis. We show, relying on the recent data of BaBar Collaboration, that the relative correction to continuum is quite small, and small correction to continuum can dramatically change the pion form factor.Comment: 12 pages, 3 figures, typos corrected, published in Phys. Lett.

The relation for transition form factors of and 0 is obtained by combining the exact nonperturbative QCD sum rule, following from the dispersive representation of axial anomaly, and quark-hadron duality. It is valid at all virtual photon momenta and allows one to express the transition form factors entirely in terms of meson decay constants. This relation is in a good agreement with experimental data.

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