We present Chandra and XMM-Newton observations of a small sample (11 objects) of optically-selected Seyfert~2 galaxies, for which ASCA and BeppoSAX had suggested Compton-thick obscuration of the Active Nucleus (AGN). The main goal of this study is to estimate the rate of transitions between transmission- and reprocessing-dominated states. We discover one new transition in NGC4939, with a possible additional candidate in NGC5643. This indicates a typical occurrence rate of at least ~0.02/year. These transitions could be due to large changes of the obscuring gas column density, or to a transient dimming of the AGN activity, the latter scenario being supported by detailed analysis of the best studied events. Independently of the ultimate mechanism, comparison of the observed spectral dynamics with Monte-Carlo simulations demonstrates that the obscuring gas is largely inhomogeneous, with multiple absorbing components possibly spread through the whole range of distances from the nucleus between a fraction of parsecs up to several hundreds parsecs. As a by-product of this study, we report the first measurement ever of the column density covering the AGN in NGC3393 (N_H ~ 4.4x10^{24} atoms/cm/cm), and the discovery of soft X-ray extended emission, apparently aligned along the host galaxy main axis in NGC5005. The latter object hosts most likely an historically misclassified low-luminosity Compton-thin AGN.
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