The Republicans start their Teruel Offensive in December 1937 with better preparation:
1-The International Brigades are brought onto the battle rather than kept in reserve as IOTL for propaganda purposes.
2-Rather than getting bogged in a very difficult urban battle for Teruel itself, the Republicans just encircle the city and continue advancing west. OTL, a major objective of this offensive was to capture the city for the propaganda hit that would be the first Republican recapture of a provincial capital. OTL the nationalist defenders of Teruel resisted for weeks in house-by-house fighting in subzero temperatures. The Republicans captured the city for a few days before a nationalist counteroffensive drove them back in January 1938.
Instead, the Republicans encircle Teruel and capture the easily defensive positions in the mountains west of the city, accomplishing their strategical goal of closing the Teruel salient that threatened the mediterranean coast. Teruel itself is besieged for months and surrenders sometime in the spring of 1938. However, with more available men, not having to deal with the Teruel meat grinder, occupying defensible positions in the mountains and threatening new offensives in the Aragon and Guadalajara fronts, the Republicans are able to easily withstand the Nationalist counteroffensive.
By the spring of 1938, the republicans have suffered much less casualties than OTL, have finally captured Teruel and have managed to keep their airforce largely intact. Now either Franco cancels the spring offensive in Aragon, that IOTL led to the nationalists reaching the mediterranean coast and splitting Catalonia away from the rest of the Republican zone, or it succeeds but the Republicans are in a much better shape when Vicente Rojo crosses the Ebro in July 1938. This allows the Republicans to win the battle of the Ebro thanks to their new soviet weapons and planes, and reconnect Catalonia with the rest of the Republican area.
By September 1938 both sides are exhausted: the Nationalists have suffered their first major strategic defeat in two years, the frontlines have barely moved for a year and the Republicans still are in no shape no start any major offensive. By late 1938, the Republicans are receiving more and more soviet supplies, but they still keep to their OTL strategy of slowly building up, resisting any major nationalist offensive and wait for the general european war that they assume will come sooner or later. This is made easier since they still control Catalonia's industry (and maybe victories in both Teruel and the Ebro give the Republican government enough political capital to be able to wrestle away the catalan factories from the anarchists). As 1939 begins, neither side is able to mount any major offensive: the Republicans are strong enough to resist but too weak to attack, and the Nationalists are unable to dislodge them from their positions around Madrid and in Aragon -and Franco's well of german and italian weapons is starting to dry as Germany now has other priorities...