A linear copolymer made of two reciprocally attracting N-monomer blocks collapses to a compact phase through a novel transition, whose exponents are determined with extensive Monte Carlo simulations in two and three dimensions. In the former case, an identification with the statistical geometry of suitable percolation paths allows one to predict that the number of contacts between the blocks grows like N9/16. In the compact phase the blocks are mixed and, in two dimensions, also zipped, in such a way to form a spiral, double chain structure.