hard to start, when started it dies down

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engine hard to start. engine cranks over, when it feels that the engine is about to catch the engine feels like it is "jumping", after a while the engines catches and runs, sometimes it dies after about three to four minutes and sometimes it stays on. Sometimes when the engine is hot, it starts right away. I adjusted the timing, replaced a bad distributor, spark plugs, a shorted intake air temp sensor, and a clogged fuel filter. I visually check that there is fuel getting into the fuel rail filter.