A few references:

DisPerSE: (see therein for references on discrete Morse theory and persistence)

• -Sousbie, T., "The persistent cosmic web and its filamentary structure - I. Theory and implementation", 2011, Monthly Notices of the Royal Astronomical Society, 414, 350

• -Sousbie, T., Pichon, C., Kawahara, H., "The persistent cosmic web and its filamentary structure - II. Illustrations", 2011, Monthly Notices of the Royal Astronomical Society, 414, 384

Books on persistence and discrete Morse-theory:

• -Zomorodian A. J., "Topology for computing", 2009, Vol. 16 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge 2, 19, 32

• -Edelsbrunner, H. & Harer, J.L., "Computational Topology", 2010

• -Gyulassy A., 2009, PhD thesis, Univ. California Berkeley 2, 8, 13

• -Forman, R., "A user’s guide to discrete morse theory", 2002

There is also a swarm of scientific articles dealing with these topics that you can find on the net, just google it :)