Eventually this dance will end. Billions of years from now the two galaxies will become one. Two galaxies don't have to bump into each other to meet. They merely have to pass close enough to get caught up in each other's gravitational stranglehold. Galaxies possess gravitational forces that can slowly pull close objects toward them.
More massive galaxies have stronger gravitational forces.
In this picture, the strong gravitational forces of the heftier galaxy, NGC 2207, lock both objects in an orbital embrace. These galaxies are the closest they've been in 40 million years. They are destined to continue swirling around each other, slowly falling closer together until the two become one beefy galaxy. Spiral galaxies contain large concentrations of gas and dust. A merger between two spirals condenses the gas clouds, igniting star birth.