The tutorials/bioconductor manuals about edgeR suggest to remove those genes does not that have at least 1 read per million in at least 'n' samples ( n = smallest group of samples). But the DESeq tutorials available doesn't include this step. Should we remove those genes or keep them in the DESeq data analysis pipeline ? This step drastically reduces the number of genes.
For example this review paper suggest to filter genes in edgeR but does not talk anything about DESeq.
Not only should you perform independent filtering, but the more recent versions of DESeq2 will do that for you automatically. For the underlying reasons, have a read through this paper, from Wolfgang Huber's group, which also produced DESeq (among other tools). See also the genefilter package in Bioconductor, which can be used in DESeq, edgeR, limma, and anything similar.
On a side note, the exact filtering done in the edgeR vignette is really just an example. I would recommend that you adjust the threshold per-experiment (the genefilter package is useful for this).