If the stocks correlate, the entire position would be closer to market neutral than not. If not correlated, not so much.
For example, if your 3 bear spredas were in the O&G sector and the other 3 were financials, it's quite possible that both threesomes could make money (or both lose) as one sector rises while the other drops. OTOH, if these were all S&P stocks, it's more likely that they would correlate somewhat and one threesome would gain and the other might lose.
And then there's individual stock news which has nothing to do with the other 5 stocks.