The geometric complex of a Morse-Bott-Smale pair and an extension of a   theorem by Bismut-Zhang
  We define the geometric complex associated to a Morse-Bott-Smale vector field, cf. [Austin-Braam, 1995], and its associated spectral sequence. We prove an extension of the Bismut-Zhang theorem to Morse-Bott-Smale functions. The proof is based on the Bismut-Zhang theorem for Morse-Smale functions, see [Bismut-Zhang, 1992]. 
Dan Burghelea and Stefan Haller