1996 vectra sri 2000cc - cuts out - eddyboy

Hi on going probs with this car,ok any one can shed some lite on this prob,new egr,new idle control,new ht leads,so far,start car up in morning,no prob,drive for miles &miles no prob,minuate turn engine off restart runs like box of nails ,rev it up a minuate or so back to ok.if do not rev up ,& just pull away it will cut out,sometimes when it feels like it,air filter fine.stumped.some one has suggested the air pump next to battery faulty,dont acturly know what part in engine this plays.many thanks if u know prob,second guessing is getting exspensive.