Caritas Christi Health Care, a chain of six hospitals owned by the Archdiocese of Boston, said it has reached a wide-ranging agreement with Local 1199 of the Service Employees International Union. The move makes Caritas the first of the region's teaching-hospital organizations to embrace the union's organizing strategy. For Caritas Christi, the accord guarantees a period of peaceful labor relations. In turn, SEIU receives a promise that management will not interfere with its organizing efforts, making it easier to unionize many of Caritas Christi's 13,000 Massachusetts employees. As part of the agreement, management will allow "free and fair" union elections.