Neccesary to pick up luggage and re-check in my second connection in US?

You don't need to pick up your luggage until the airport it's checked through to, with one exception: You must carry it through US Customs when entering the US.

At your departure airport, the bag will be checked through to your final destination, but even so, everyone must pick up and carry their bags through US Customs at their first port of entry, and then immediately drop them again at a special baggage drop just past the customs area. They then return to baggage handling and will be routed to wherever they were checked through to.

There are a few very rare itineraries in the US where you will go through immigration at one airport and customs at another airport. This is called progressive clearance. It's generally used on itineraries which enter the US, making two or more landings, and then depart the US. Passengers will be notified if progressive clearance applies to their itinerary. In this case, immigration will return your landing card to you and you will be instructed to claim your checked baggage and present it to customs at the next airport.

As soon as you have legally entered the US, got your passport stamp from the border officials and either got questioned by customs agents or not, you are in the US and are treated like any other domestic traveller. Typically, your luggage will be checked through at your first departure point to its final destination, but the customs bit when entering the states does not influence that.

So say your itinerary is London–New York–Chicago–Denver.

1. Arriving in New York, you need to pass immigration and take your bag through customs then drop it off again. The question indicates you know this and it is well documented across Travel Stack Exchange. You then normally board your flight to Chicago. Remember that your luggage still has tags for Denver.

2. Arriving at Chicago, nobody at the airport (unless they really want to look it up) will be able to differentiate your itinerary from a domestic one New York–Chicago–Denver. Thus, you will be treated like any domestic transfer passenger. You will not see your luggage, just move on to the gates for your next flight. You will also not see any immigration or customs at the airport.

3. Arriving at Denver, well; you’re through.

The same applies on your way back. You will be treated as a domestic passenger until your last (international) leg. You will not see your luggage at New York, and there is no need as there are no ‘exit customs inspections’.

Of course, there is always the possibility that your bags are short-checked (typically upon passenger’s request for overnight layovers). This would mean that check-in tells you your bag will only be checked through to Chicago where you would have to collect it and recheck it later. A common scenario for this is an overnight layover: you may want a fresh change of clothes at the airport. However, this is the less common scenario.

In any case, it is always a good idea to confirm by asking at check-in (assuming a manned check-in or luggage drop-off) or to check the bag labels. They will state the furthest destination you’re going to.

There is an important exception to this rule: if you fly to the U.S. from a preclearance airport, your luggage will typically be checked through to the final destination, and you won't have to collect it at your first U.S. stop.

At these airports, you clear U.S. customs and immigration in the country you are departing, rather than on arrival in the U.S., so the flight effectively operates as a U.S. domestic flight: you simply land in the U.S. and get off the plane, with no controls.

(You also don't have to collect the luggage that the pre-clearance airport itself, at least in all cases I'm aware of, because they have systems for associating the luggage with you and doing a customs check. In some places, for example, you may be shown the checked bag on a screen.)

Here is the complete list of pre-clearance airports. In brief, they include:

• All major airports in Canada
• A few major destinations in the Carribean
• Dublin and Shannon in Ireland
• Abu Dhabi

Flying via a pre-clearance airport is a good option to explore when available, because it tends to be a better experience. Not just because of the luggage, but also because immigration and customs in the preclearance location can be a lot less busy than in a major U.S. airport, and U.S. connections are easier: you land in a domestic terminal and then simply continue on to your onward domestic flight. We often choose Dublin for this reason when flying out of Europe.