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Although the luminosity growth for Tevatron Run II was slower than expected, steady growth of luminosity has been demonstrated during the last three years with the peak luminosity of 1.02 x 10{sup 32} cm{sup -2} s{sup -1} achieved in July 2004. Suppression of instabilities has been a valuable contributor to the luminosity growth. This report discusses the transverse instabilities in the Tevatron and Recycler.