My German neighbour has planted ths small tree, but I can't identify it. Could you please help me? Thanks.
Thank you but what species? We have the common European hawthorn here (Crataegus monogyna, in Italian biancospino) but it's different from this one.
Like another rose family genus Rubus the North American hawthorns in particular present numerous difficulties - see narrative here: Crataegus in Flora of North America @ efloras.org
Agree with one of the North American hawthorns; it isn't any of the European hawthorns, but several American species (and hybrids!) are grown in Europe as ornamental trees.
As already alluded to, identification of North American hawthorns can be frustratingly tricky (witness the Flora of North America account of the genus), but your neighbour's tree is reminiscent (at least to me) of Crataegus pennsylvanica. We had a specimen of that species in UBC Botanical Garden (at the far end of the parking lot) for many years. It was a wonderful, thornless, disease-resistant tree that regularly produced copious amounts of very attractive, large orange edible haws. There is a shrubbier and thornier species with similar leaves and fruit, C. submollis (but now I'm getting into dangerous territory with suggestions). Regardless of what species the tree might be, it would be interesting to know how it got to Tuscany.
Several of them are grown as ornamental trees in Europe. Not sure if any have become invasive anywhere, but I'd not be too surprised if they did.