By Jennifer Ludden , Anusha Mathur Two halves of a four-bedroom factory-built home are pushed together in Petersburg, Virginia. It's one of dozens of such homes being set on permanent foundations and will blend in with other single-family houses in the neighborhood. Anusha Mathur/NPR hide caption PETERSBURG, Va. — At first glance, the house parked on a muddy lot along a residential street not far from City Hall looks like it has been ripped apart right down the middle. But the opposite is happening. A construction team is pushing together two halves of a brand-new factory-built house in the middle of this neighborhood of small single-family homes. Once it's set, with its pitched roof and front porch, it won't look like anyone's stereotype of a mobile home. Across the street, two big trucks roll in from Pennsylvania to deposit another house, this one with blue siding and beige window shutters. For decades, manufactured homes have faced stigma and been confined to trailer parks.…