  We investigate the transition scale to homogeneity, $R_H$, using as cosmic
tracer the spectroscopic sample of blue galaxies from the Sloan Digital Sky
Survey (SDSS). Considering the spatial distribution of the galaxy sample we
compute the two point correlation function $\xi(r)$, the scaled counts in
spheres $\mathcal{N}(<r)$, and the fractal dimension $\mathcal{D}_2(r)$ to
quantify the homogeneity scale in the Local Universe ($0.04 < z < 0.20$). The
sample in analysis is compared with {\it random} and {\it mock} catalogues with
the same geometry, and the same number of synthetic cosmic objects as the
dataset, to calculate the covariance matrix for the errors determination. The
criteria adopted for the transition-to-homogeneity follows the literature, it
is attained when $\mathcal{D}_2(r)$ reaches the $1$ per cent level of the limit
value $3$ (i.e., where it reaches $2.97$) as the scale increases. We obtain
$R_H = 70.33 \pm 10.74$ Mpc$/h$, at the effective redshift
$z_{\text{eff}}=0.128$, for a sample containing $150\,302$ SDSS blue galaxies
with $0.04 < z < 0.20$. Additionally, we perform robustness tests by analysing
the homogeneity scale in sub-volumes of the original one, obtaining coherent
results; we also check for a possible artefact in our procedure examining a
homogeneous synthetic dataset as a pseudo-data, verifying that such systematic
is absent. Because our analyses concentrate in data at low redshifts, $z <
0.20$, we find interesting to use cosmography to calculate the radial comoving
distances; therefore in this subject our analyses do not use fiducial
cosmological model. For completeness, we evaluate the difference of the
comoving distances estimation using cosmography and fiducial cosmology.
