If we were to consider the universe to be static in a stationary frame, and we are moving at some large relative speed to that frame, then the light we receive from the stars in front of us would be blueshifted. If we were to then decelerate in the opposite direction of our line of travel, then the distances between stars and galaxies would appear to become greater, the distances expanding equally to the front and back of us at least, but we would still be travelling toward the stars in front of us at the same time that they are "expanding" away. The stars closest to us will always remain blueshifted to some degree as we decelerate until we pass the point of rest in the stationary frame and begin moving in the opposite direction, whereas the closest stars in the opposite direction will then become blueshifted instead.
Upon further reflection, though, and what you replied, I'm now saying only the stars closest to us will remain blueshifted whereas in my last post I said the stars directly along the line of travel in front of us would all be blueshifted by the same amount regardless of the distance. I was thinking before that only the instantaneous relative speed to the stars, or to the stationary frame in general, would be all that mattered as far as the redshift or blueshift goes, but now I realize that if all distances expand to the same degree upon deceleration, then stars at twice the distance will have the appearance of moving away twice as fast with twice the redshift and so forth, just like the Hubble relationship after all, so there must be something to do with the simultaneity shift during deceleration there which determines different measured relative speeds at different times that varies with distance. Considering this, the original blueshift for stars at any distance, due to our initial inertial relative speed, will only add to that, then, while it seems the redshift should indeed increase with greater distance during deceleration, making the blueshift a local effect only, so it would seem an overall redshift in all directions at large distances would indeed predominate, which tends to agree with what you were saying after all. Oops. Sorry about that.
Thinking about it even further, though, as we decelerate, if the distance between the stars appears to be expanding, then their relative speeds away from us also becomes greater with greater distance, so even our own relative speed to the stationary frame is not an invariant except locally, since it varies with distance to individual stars even though the stars themselves are stationary to each other, so the rate of expansion between stars may not be constant either, but vary with distance as well. If stars that are very far away cannot recede faster than the speed of light relative to us, then they would be travelling away at a lesser rate than a direct Hubble expansion rate. You're right, this is confusing.
Here's one more thing. As we decelerate back into the stationary frame, if we were to stop the deceleration by simply turning off our engines (not considering gravity pulling us back while we travel inertially forward but by engines instead) when we reach the point of rest with a static universe, then everything should then be observed as stationary to each other as we are once again stationary to it as well. That appears to mean that while we were travelling forward inertially, everything else in the universe was travelling toward us at the same time and the deceleration cancels that effect. In other words, while we were travelling forward inertially, everything would appear contracted toward us along our line of travel compared to the distances observers in the stationary frame would measure, but it appears it should also mean that everything is moving toward us at a faster rate with greater distance along our line of travel in both directions, in order to be cancelled out upon decelerating back to rest when the stars are then "expanded" away from us until they reach their initial state of rest relative to us. I don't think I've ever heard anything like that with Relativity except for the Rindler horizon behind us, which might apply here, but I'm not sure how to think about it, since it would have to apply in front of us as well. It's getting complicated.
Richard, help!