Let me give you a better answer on this. The sphere at the back of the picture is a vacuum reservoir for the HVAC actuators. They are vacuum driven. The sphere stores vacuum for times when the engine has low manifold vacuum (like when at wide open throttle). Without it, at times of low manifold vacuum, the vacuum actuated doors will close as they don't have enough engine vacuum to keep them open. For example, the defrost door will close and the air flow will be directed away from blowing on you to blowing on the windshield through the defroster vents.
The evaporative emissions canister is the object you have circled at the lower left corner of your picture. The vent line from the fuel tank connects to it. It's purpose is to store fuel vapor from the fuel tank and then under certain conditions (based on engine temperature, load and throttle position, the canister is purged and the fuel vapor is sucked into the carburetor and burned in the engine. Obvoiusly it's not going to work this way for an LS swap.
If you eliminate the canister, you will need to put something on the vent line to "catch" the fuel fumes or the car will smell of gas in the garage, particularly when the garage is warm. Some have removed the canister and simply put a small breather filter on the end of the first section of the vent line under the rear of the car near the rear end. They have reported good results with this approach.
Another option is to keep the canister and vent it to the air intake for the LS. This is what we did on my brother's 78 Z28 when we LS swapped it. The canister that was stock to his car had four or six places for vacuum lines so we elected to replace it with a much simpler unit that just had one port in and one port out. We had already replaced the fuel and brake lines on the car with new stainless steel lines when we decided we were going to do an LS swap. The fact that a brand new stainless vent line was already in place contributed to our decision to go this way. We simply have the canister venting to the end of the K&N filter on the air intake. You can't see the vapor canister because it is hidden by the windshield washer tank but this is the best pic I have....
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The canister we used is pretty similar to or is the same as this one...
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We are planning to build an "airbox" for the car to shield the air filter from engine heat and to where the engine is breathing cold air. When we do, we'll just connect the hose to that "airbox".
The car is old enough that the presence of all original emissions equipment is not a requirement to pass the state inspection here in Texas. Instead, they are only doing a safety inspection on it. If you eliminate it, it will still pass inspection. Still I encourage you to keep it but if you need the room for a cold air intake or just don't want to see it, then you'll want to do something to deal with the fuel vapor. The deal that
superbon54 posted is very nice but lord that is spendy. That's coming from me, a spend thrift. His build is unbelievably nice though. Hope this helps.