All proceedings at law or in equity relating to the doing of the work of the said public improvement or works authorized by this article and necessary or property to accomplish the purposes contemplated by the provisions of this article, shall be instituted or taken and conducted in the joint corporate names of all the municipalities contracting for such public improvement or works, and when authorized or approved by the joint meeting herein provided for, shall be deemed taken and construed to have been taken and done for the proportionate benefit of all such contracting municipalities in accordance with the terms of the contract between them.