In all the sound,(area 6 is considered inshore,) you can lobster recreationaly, off the south shore there is a 3 mile limit to state waters,past that you need to be commerical with a fed permit.
The rules for both state and fed state pots and traps must be marked with float/flags with owners name and permit # clearly attached
Just a quick cut and paste for you from the DEC:
§44.2 Identification of gear used in taking of lobsters
Gear used in taking lobsters must be identified as follows:
(a) All lobster pots or traps, while in operation, must have attached to them a floating buoy or identification marker which must be constructed and placed as to be clearly visible on the surface of the water. Plastic containers, bottles or jugs originally designed to contain liquids must not be used as buoys or markers to identify the location of lobster pots or traps.
(b) Each buoy or marker attached to a lobster pot or trap must be of a distinctive color. The number, including any letters, assigned the holder of a lobster permit for the current year at the time he or she obtains a lobster permit must be painted or otherwise affixed on each buoy or marker in a contrasting color, or branded on each buoy or marker, in clearly visible characters not less than two inches in height. The same color or combination of colors must be used on all buoys or markers bearing the same permit number.
(c) The same number appearing on a buoy or marker shall also be marked or branded, in characters not less than three-fourths inch in height, on all pots or traps identified by that buoy or marker. If the construction of a pot or trap does not allow it to be marked by branding, that pot or trap shall be marked by a tag or other device bearing, in clearly visible and legible characters, the same number appearing on a buoy or marker used to identify that pot or trap. This tag or other device shall be of a material that is not deteriorated by sea water and shall be firmly attached to the pot or trap it identifies. A valid trap tag is an acceptable identifying marker as long as it contains the fishermen's New York State commercial lobster harvester's permit number.
(d) Lobster pots shall not be placed within 25 feet of designated navigation channels, and all floating buoys or identification markers and lines attached to such pots shall remain outside designated navigation channels at all times.
Notice in part A about the float must be clearly visible on the surface.
The west coast dosn't have these regs that's why the supply of Tr's comes from there.