(b) To further enable the fund to realize its public and governmental purpose, the fund may enter into agreements with the transportation authority, to which the transit authority may be a party, for planning, design and feasibility studies, provided or caused to be provided by the transportation authority.

(c) Neither the state, nor the city, nor the transit authority shall be liable for any rentals or other payments payable by the fund to the transportation authority pursuant to the terms of any lease or other agreement entered into by the fund under this title; and the city shall not be required to pay for all or part of the cost of any transit facility provided pursuant to this title. Any such lease or other agreement shall contain among its terms a statement to that effect.

(d) A schedule of transit facilities authorized to be provided by the fund in accordance with the provisions of this title may be adopted as hereinafter provided, and the fund shall not enter into any lease or other agreement obligating the fund to pay money to the transportation authority unless such lease or other agreement shall relate to a transit facility contained in such schedule; nor unless, in the case of a transit facility which consists of a rapid transit railroad or portion thereof, a route and general plan for such transit facility shall have been previously approved pursuant to the provisions of the rapid transit law. The mayor, city council and city board of estimate shall have the power to adopt, veto, and amend such schedule and the amounts stated therein in the same manner provided under the city charter for capital projects. Such schedule shall not be deemed a part of the city's capital budget and the transit facilities contained in such schedule shall not be deemed city capital projects. Such schedule shall be published together with the capital budget accompanied by a statement to this effect. Such schedule shall specify the maximum amount of indebtedness secured by and payable from rental or other payments receivable from the fund which the transportation authority may incur with respect to each transit facility therein set forth. The fund shall not enter into any lease or other agreement which provides or contemplates that the transportation authority shall incur such indebtedness (i) which, for any such transit facility would exceed the amounts specified in such schedule, which amount shall not be reduced or rescinded except by amendment and shall in no event be reduced or rescinded by the city after such lease or other agreement has been executed without the written consent of the transportation authority, or (ii) which would bring the aggregate amount of such indebtedness of the transportation authority incurred pursuant to this title to an amount in excess of two hundred fifty million dollars. Notwithstanding any other limitation herein prescribed, the mayor shall increase the amount so specified for any such transit facility by the amount necessary to pay judgments, claims or awards including interest thereon against the transportation authority arising out of work undertaken pursuant to any such agreement, and the mayor may increase the amount so specified by not more than fifteen per cent in order to meet any costs required to complete such transit facility, or by any amount required to complete such transit facility when the cost to complete such transit facility has increased due to catastrophe. In the event that the mayor shall increase the amount so specified for any such transit facility for any of the foregoing reasons, the limitation on the aggregate amount of such indebtedness of the transportation authority which may be outstanding at any one time shall be increased by the same amount. In calculating the aggregate amount of such indebtedness of the transportation authority which may be increased pursuant to this title, there shall be excluded the amount of outstanding obligations to be refunded or received from the proceeds from the sale of, or to be exchanged for new obligations. Nothing herein contained shall be construed to require the fund or the transportation authority to enter into any lease or other agreement relating to one or more of the transit facilities contained in such schedule.