Nynex Corp. on Tuesday signed an agreement with Sprint Communications to offer long-distance service. As part of the two-year contract, Nynex will purchase network, customer care, billing and telemarketing services from Sprint for marketing long-distance service. Nynex plans to offer the service within the next three months in Arizona, California, Florida, Georgia, Illinois and Texas. Nynex said it will use direct mail and targeted print ads to promote the service. Ogilvy & Mather, New York, is agency of record for Nynex.