Relationship between the $\gamma-$ray variability and the pc-scale jet in the blazar 3C 454.3

3C 454.3 is a flat spectrum radio quasar (FSRQ) known for its high variability across the electromagnetic spectrum, showing structural and flux variability in its pc-scale jet, and correlated variability among frequency bands. This study aims to identify the structure, dynamics, and radiative processes common to the innermost regions of the blazar 3C 454.3. We investigate whether any jet component can be associated with $\gamma-$ray emission and variability. We analyze the relationship between the variable $\gamma-$ray emission and pc-scale jet properties in 3C 454.3 by combining $\gamma-$ray data spanning twelve years with contemporaneous VLBA multi-epoch images at 15 and 43 GHz. Spearman rank correlation tests are conducted to determine if the flux variability of any jet component is associated with $\gamma-$ray variability. Core emission at 43 and 15 GHz strongly correlates with $\gamma-$ray emission. The 43 GHz core (Q0) contributes around 37$\%$ of the observed $\gamma-$ray variability, while the 15 GHz core (K0) accounts for 30$\%$. A quasi-stationary component at 43 GHz, at a projected distance of 4.6 pc, correlates with the $\gamma-$ray flux, accounting for 20$\%$ of its emission between 2016 and 2021. We found a mobile component (Q3 between 2010.18 and 2011.16) at 43 GHz with a projected distance between 0.8 and 2.3 pc and apparent velocity of $\beta_{app} = 9.9 \pm 1.1$ c, accounting for approximately 28% of the $\gamma-$ray emission. The observed simultaneous variability in emission regions beyond the central parsec strongly suggests synchrotron self-Compton (SSC) as the primary mechanism for $\gamma-$ray production in these regions. Our findings demonstrate the existence of multiple $\gamma-$ray emission regions within the blazar jet but also suggest that some of these regions are non-stationary over time.