The inversion or excision of a DNA sequence or the integration of a foreign DNA sequence into a homologous genomic site. These all require homologous recombination at the sites of inversion, excision or integration, and contrast with transposition, in which a DNA sequence is inserted or removed from a non-homologous site by excision of the donor sequence from its source, cutting open the acceptor site, and insertion of the transposed sequence and its ligation in place.