Established in 1995, the owners of safeway moving & storage saw a need for professional moving services in lexington, ky. Safeway partnered with mayflower transit, the most recognized name in the industry, to bring the best service available to our customers. Safeway moving & storage, inc. Is a company comprised of the most dedicated, organized, professional and friendly moving specialists in the industry. Our trained professional employees go to great lengths, moving you anywhere with the utmost care. Specializing in household and commercial moves, we can handle all of your moving needs. Mayflower transit, founded in 1927, is one of the nation’s oldest and largest moving companies.