The underlying principle is easy enough: a state offers residency rights to non-citizens who place a minimum sum in housing. The qualifying amount varies widely between countries, and the authorities adjust it regularly.
A crucial distinction divides residence and a passport. The permit allows you to live there, generally on a renewable basis, but citizenship normally requires far more time and additional conditions. An agent's promise of citizenship in return for an apartment purchase is a warning sign.
Past the headline threshold, such permits come with additional requirements. Common ones cover a police clearance certificate, health cover, evidence of sufficient means and a minimum stay on local soil annually. Ignoring one of these can cost you the residency while you still own the home.
Tax residency forms an entirely separate matter. Having residency does not necessarily make you taxable on worldwide income, though crossing the day-count threshold frequently does. A number of states rely on a threshold based on days spent locally, and the implications touch income earned elsewhere.
The realistic approach is essentially straightforward: choose the montecatini-terme property prices first, and let the permit be the second reason. Such schemes get restructured from time to time, and an apartment bought only houses for sale in usa paperwork proves hard to rent and hard to resell.